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• 23:21, 22 October 2023 C7X talk contribs created page User talk:RhubarbJayde/REL-NPR (Subdivision candidates: new section) Tag: New topic
• 06:36, 2 October 2023 C7X talk contribs created page Correct cardinal (Created page with "A \(\Sigma_n\)-correct cardinal is a cardinal \(\kappa\) such that \(V_\kappa\) is a \(\Sigma_n\)-elementary substructure of \(V\), where \(\Sigma_n\) is from the Lévy hierarchy.{{citation needed}} A regular cardinal is \(\Sigma_2\)-correct iff for every first-order formula \(\phi(x)\) and any \(x\in H_\kappa\), if \(\exists\alpha(H_\alpha\vDash\phi(x)\)<ref>, then there is a \(\beta<\kappa\) such that \(H_\beta\vDash\phi(x)\). [https://logicdavid.github.io/files/mthes...")
• 13:47, 19 September 2023 C7X talk contribs created page Uniformity (Created page with "Uniformity is a justification used for existence of some very large large cardinals, such as measurable and strongly compact cardinals. As there is no current characterization of measurable cardinals by closure under certain operations as there are with some smaller large cardinals, uniformity is often the method of choice for justifying their existence.<ref name="MaddyI">P. Maddy, "[https://www.cs.umd.edu/~gasarch/BLOGPAPERS/belaxioms1.pdf Believing the Axioms I]", pp.5...")
• 01:57, 8 September 2023 C7X talk contribs created page Talk:Countability ("Furthermore, a gap ordinal may have a map to N but this map can not be defined at all using first-order set theory": new section) Tag: New topic
• 23:34, 7 September 2023 C7X talk contribs created page Talk:Powerset (Naturality of CH: new section) Tag: New topic
• 20:20, 4 September 2023 C7X talk contribs created page Talk:Continuum hypothesis ("unsolved problems of set theory": new section) Tags: Mobile edit Mobile web edit New topic
• 23:15, 31 August 2023 C7X talk contribs created page Talk:Proper class ("because that would cause a paradox": new section) Tag: New topic
• 22:57, 31 August 2023 C7X talk contribs created page Talk:Zero sharp ("Totally stable": new section) Tag: New topic
• 22:42, 31 August 2023 C7X talk contribs created page Cardinal (Created page with "Cardinals are an extension of the natural numbers that describe the size of a set. There are two ways to define cardinality: cardinals as initial ordinals, or cardinals as equivalence classes under bijectability. The second is more common in settings without the axiom of choice, since not all sets are necessarily well-orderable.{{citation needed}} The aleph numbers are examples of well-ordered cardinals, and exhaust the infinite well-ordered cardinals.{{citation nedede...")
• 21:40, 29 August 2023 C7X talk contribs created page Gap ordinal (Created page with "A gap ordinal is an ordinal \(\alpha\) such that \((L_{\alpha+1}\setminus L_\alpha)\cap\mathcal P(\omega)=\varnothing\).<ref name="MarekSrebrny73">W. Marek, M. Srebrny, "[https://www.sciencedirect.com/science/article/pii/0003484374900059 Gaps in the Constructible Universe]" (1973). Annals of Mathematical Logic vol. 6, pp.359--394.</ref>^p.364 An ordinal \(\alpha\) is said to start a gap if \(\alpha\) is a gap ordinal but for all \(\beta<\alpha\), \((L_\alpha\se...")
• 21:15, 29 August 2023 C7X talk contribs created page Talk:Weakly compact cardinal ("A relatively convoluted definition": new section) Tag: New topic
• 20:42, 2 March 2023 C7X talk contribs created page Admissible (Created page with "A set \(M\) is admissible if \((M,\in)\) is a model of Kripke-Platek set theory. An ordinal \(\alpha\) is admissible if there exists an admissible set \(M\) such that \(M\cap\textrm{Ord}=\alpha\). This definition of admissibility is equivalent to \(L_\alpha\vDash\textrm{KP}\).<ref>Probably in Barwise somewhere</ref>")
• 02:33, 29 November 2022 C7X talk contribs created page Buchholz's psi-functions (Created page with "Buchholz's \(\psi\)-functions are a family of functions \(\psi_\nu:(\omega+1)\times\textrm{Ord}\to\textrm{Ord},\;\alpha\mapsto\psi_\nu(\alpha)\) defined by Wilfried Buchholz in 1984. ==Historical background== In 1950, H. Bachmann defined the first ordinal collapsing function, Bachmann's \(\varphi\). While able to succinctly describe the Bachmann-Howard ordinal as \(\varphi_{\varepsilon_{\Omega+1}}(0)\), Bachmann's \(\varphi\) had a complicated definition Possible source...")
• 02:53, 16 October 2022 C7X talk contribs created page Fodor's lemma (Created page with "'''Fodor's lemma''' (or the '''pressing-down lemma''') is a lemma proven by Géza Fodor in 1956. The lemma states that when \(\kappa\) is an uncountable regular cardinal and \(S\) is a stationary set of ordinals \(<\kappa\), any regressive function \(f:S\to\{<\kappa\}\) must be constant on a stationary set of ordinals \(<\kappa\). ==Importance to apierology== Since \(\omega_1\) is regular, setting \(S=\{<\omega_1\}\), Fodor's lemma implies there does not exist a fundame...")
• 21:26, 5 September 2022 C7X talk contribs moved page List of ordinals to List of countable ordinals
• 21:25, 5 September 2022 User account C7X talk contribs was created automatically