- 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...
-
Tzouvaras (2003). Moss,
Lawrence S. (2018), Zalta,
Edward N. (ed.), "Non-
wellfounded Set Theory", The
Stanford Encyclopedia of
Philosophy (Summer 2018 ed...
-
formal logic,
wellfoundedness prohibits ⋯ < x < ⋯ < x < ⋯ {\displaystyle \cdots <x<\cdots <x<\cdots } for any x. Thus non-
wellfounded mereology treats...
- 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, p. 306, ISBN 1575860090...
- 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 ****erting that the
ordinal called ε0 is
wellfounded; see Gentzen's
consistency proof. Gentzen's
theorem spurred the development...
-
other set
theories such as the
various constructive set
theories or non-
wellfounded set theory. (Woodin) Does the
generalized continuum hypothesis below...
-
theory obtained by
removing the
axiom of
regularity from ZFC.
Various non-
wellfounded set
theories allow "safe"
circular sets, such as
Quine atoms, without...
-
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...
