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In mathematics, a binary relation R is called well-founded (or wellfounded or foundational) on a set or, more generally, a class X if every non-empty...

formal logic, wellfoundedness prohibits ⋯ < x < ⋯ < x < ⋯ {\displaystyle \cdots <x<\cdots <x<\cdots } for any x. Thus non-wellfounded mereology treats...

 110. Nitta, Okada & Tzouvaras (2003). Moss, Lawrence S. (2018), "Non-wellfounded Set Theory", in Zalta, Edward N. (ed.), The Stanford Encyclopedia of...

extension of S ◃ P {\displaystyle S\triangleleft P} is the W-type (type of wellfounded trees) W s : S P s {\displaystyle {\mathsf {W}}_{s:S}\,P\,s} of Martin-Löf...

κ-model M for which there exists an M-ultrafilter on κ which allows for wellfounded iterations by ultrapowers of arbitrary length. Gitman gave a finer notion...

system that includes an axiom asserting that the ordinal called ε0 is wellfounded; see Gentzen's consistency proof. Gentzen's theorem spurred the development...

conflicting class of models, such as the various constructive resp. non-wellfounded set theories, etc. Does the partition principle (PP) imply the axiom...

K. J. & Moss, L. (1996) Vicious Circles. On the Mathematics of Non-Wellfounded Phenomena ISBN 1-57586-008-2 Barwise, K, J. & Seligman, J. (1997) Information...

Moss, Lawrence S. (1996), Vicious circles. On the mathematics of non-wellfounded phenomena, CSLI Lecture Notes, vol. 60, CSLI Publications, ISBN 1575860090...

and an added condition of iterability (referring to the existence of wellfounded iterated ultrapowers): a mouse is then an iterable premouse. The notion...

{\displaystyle \langle \mu _{x\upharpoonright n}\mid n\in \omega \rangle } is wellfounded. An equivalent definition is produced when the final condition is replaced...

Driving High Blood Pressure — WellFounded - Founders Health & Concierge Performance Medicine | CHHP Longevity Research". WellFounded - Founders Health & Concierge...

identity function on the type X. Moerdijk, Ieke; Palmgren, Erik (2000). "Wellfounded trees in categories". Annals of Pure and Applied Logic. 104 (1–3): 189–218...

Ahrens, Benedikt; Capriotti, Paolo; Spadotti, Régis (2015-04-12). Non-wellfounded trees in Homotopy Type Theory. Leibniz International Proceedings in Informatics...

theory obtained by removing the axiom of regularity from ZFC. Various non-wellfounded set theories allow "safe" circular sets, such as Quine atoms, without...

Mathematics Genealogy Project Moss, Lawrence S. (February 20, 2018). "Non-wellfounded Set Theory". In Zalta, Edward N. (ed.). The Stanford Encyclopedia of...

ISSN 1572-8420. COTNOIR, AARON J.; BACON, ANDREW (2011-12-09). "Non-Wellfounded Mereology". The Review of Symbolic Logic. 5 (2): 187–204. doi:10.1017/s1755020311000293...

^{|b|}:(f\circ \pi _{ba})(t)\in t\}\in E_{b}.} (Wellfoundedness) The limit ultrapower Ult(V,E) is wellfounded (where Ult(V,E) is the direct limit of the ultrapowers...

II. Math. Japon. 45 (1997), no. 3, 555–571. Kanovei, Vladimir; On non-wellfounded iterations of the perfect set forcing. Journal of Symbolic Logic 64 (1999)...

theologian, "might have serious difficulties, for reasons which appear to him wellfounded, in accepting a non-irreformable magisterial teaching." In such a case...

collections, and all sets (collections which are contained in a level) are wellfounded. No theorem in Potter would be overturned if an axiom stating that all...

Agda and Rocq), then final types (codata) may contain infinite, non-wellfounded values, whereas initial types (data) do not. On the other hand, if the...

the tree T {\displaystyle T} . A tree that has no branches is called wellfounded; a tree with at least one branch is illfounded. By Kőnig's lemma, a tree...