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"published": "2023-08-14T21:44:56Z",
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"content": "<p>Index of selected threads on <a href=\"https://mathstodon.xyz/tags/hott\" class=\"mention hashtag\" rel=\"tag\">#<span>hott</span></a> <a href=\"https://mathstodon.xyz/tags/constructive\" class=\"mention hashtag\" rel=\"tag\">#<span>constructive</span></a> <a href=\"https://mathstodon.xyz/tags/math\" class=\"mention hashtag\" rel=\"tag\">#<span>math</span></a></p><p>* 2022/10/31. Proofs by contradiction.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/109264034964990196\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">109264034964990196</span></a></p><p>* 2022/11/12. Synthetic topology of data types and classical spaces.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/109332986014534390\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">109332986014534390</span></a></p><p>* 2022/11/14. Notions of space.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/109343930842850773\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">109343930842850773</span></a></p><p>* 2022/11/16. Trichotomy of ordinals.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/109355604029879269\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">109355604029879269</span></a></p><p>* 2022/11/22. Birthday present by Tom de Jong.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/109388875794058555\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">109388875794058555</span></a></p><p>* 2022/11/23. Concrete example illustrating that constructive mathematics is more general than classical mathematics.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/109395006766077334\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">109395006766077334</span></a></p><p>* 2022/12/01. Combinatorial game theory.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/109440314312765877\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">109440314312765877</span></a></p><p>* 2022/12/08. Universe polymorphic type systems.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/109480057029596732\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">109480057029596732</span></a></p><p>* 2022/12/08. Why cubical type theory, and why cubical Agda?<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/109480455436886869\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">109480455436886869</span></a></p><p>* 2022/12/20. The axiom of choice in HoTT/UF.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/109546988519874380\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">109546988519874380</span></a></p><p>* 2022/12/22. A common generalization of the univalence axiom and the K axiom.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/109558670025171863\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">109558670025171863</span></a></p><p>* 2023/02/03. Defining large numbers without using induction.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/109802885041067972\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">109802885041067972</span></a></p><p>* 2023/02/10. Several kinds of categories in HoTT/UF.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/109842791175514936\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">109842791175514936</span></a></p><p>* 2023/03/03. Universes in type theory as mathematical objects interesting in their own right.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/109961534132268566\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">109961534132268566</span></a></p><p>* 2023/03/22. Playing rationally against irrational players.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/110068977445045121\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">110068977445045121</span></a></p><p>* 2023/04/11. What are universes for in HoTT/UF?<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/110181596099423100\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">110181596099423100</span></a></p><p>* 2023/06/02. Ayberk's predicative version of the patch locale of a Stone locale.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/110476555405397697\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">110476555405397697</span></a></p><p>* 2023/06/07. Github project TypeTopology.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/110504563233350460\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">110504563233350460</span></a></p><p>* 2023/06/15. Constructive notions of disjunction.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/110549967500023998\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">110549967500023998</span></a></p><p>* 2023/07/09. Trichotomy of the reals constructively.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/110685074921103237\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">110685074921103237</span></a></p><p>1/</p>",
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"en": "<p>Index of selected threads on <a href=\"https://mathstodon.xyz/tags/hott\" class=\"mention hashtag\" rel=\"tag\">#<span>hott</span></a> <a href=\"https://mathstodon.xyz/tags/constructive\" class=\"mention hashtag\" rel=\"tag\">#<span>constructive</span></a> <a href=\"https://mathstodon.xyz/tags/math\" class=\"mention hashtag\" rel=\"tag\">#<span>math</span></a></p><p>* 2022/10/31. Proofs by contradiction.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/109264034964990196\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">109264034964990196</span></a></p><p>* 2022/11/12. Synthetic topology of data types and classical spaces.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/109332986014534390\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">109332986014534390</span></a></p><p>* 2022/11/14. Notions of space.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/109343930842850773\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">109343930842850773</span></a></p><p>* 2022/11/16. Trichotomy of ordinals.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/109355604029879269\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">109355604029879269</span></a></p><p>* 2022/11/22. Birthday present by Tom de Jong.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/109388875794058555\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">109388875794058555</span></a></p><p>* 2022/11/23. Concrete example illustrating that constructive mathematics is more general than classical mathematics.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/109395006766077334\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">109395006766077334</span></a></p><p>* 2022/12/01. Combinatorial game theory.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/109440314312765877\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">109440314312765877</span></a></p><p>* 2022/12/08. Universe polymorphic type systems.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/109480057029596732\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">109480057029596732</span></a></p><p>* 2022/12/08. Why cubical type theory, and why cubical Agda?<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/109480455436886869\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">109480455436886869</span></a></p><p>* 2022/12/20. The axiom of choice in HoTT/UF.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/109546988519874380\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">109546988519874380</span></a></p><p>* 2022/12/22. A common generalization of the univalence axiom and the K axiom.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/109558670025171863\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">109558670025171863</span></a></p><p>* 2023/02/03. Defining large numbers without using induction.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/109802885041067972\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">109802885041067972</span></a></p><p>* 2023/02/10. Several kinds of categories in HoTT/UF.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/109842791175514936\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">109842791175514936</span></a></p><p>* 2023/03/03. Universes in type theory as mathematical objects interesting in their own right.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/109961534132268566\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">109961534132268566</span></a></p><p>* 2023/03/22. Playing rationally against irrational players.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/110068977445045121\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">110068977445045121</span></a></p><p>* 2023/04/11. What are universes for in HoTT/UF?<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/110181596099423100\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">110181596099423100</span></a></p><p>* 2023/06/02. Ayberk's predicative version of the patch locale of a Stone locale.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/110476555405397697\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">110476555405397697</span></a></p><p>* 2023/06/07. Github project TypeTopology.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/110504563233350460\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">110504563233350460</span></a></p><p>* 2023/06/15. Constructive notions of disjunction.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/110549967500023998\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">110549967500023998</span></a></p><p>* 2023/07/09. Trichotomy of the reals constructively.<br /><a href=\"https://mathstodon.xyz/@MartinEscardo/110685074921103237\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/@MartinEscardo/</span><span class=\"invisible\">110685074921103237</span></a></p><p>1/</p>"
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