In mathematics, the wholeness axiom is a strong axiom of set theory introduced by Paul Corazza in 2000.[1]
^Corazza, Paul (2000), "The Wholeness Axiom and Laver Sequences", Annals of Pure and Applied Logic, 105 (1–3): 157–260, doi:10.1016/s0168-0072(99)00052-4
Wholenessaxiom, rank-into-rank (Axioms I3, I2, I1, and I0) The following even stronger large cardinal properties are not consistent with the axiom of...
An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments...
reflection principles are implied by known large cardinal axioms. An example of this is the wholenessaxiom, which implies the existence of super-n-huge cardinals...
psychiatrist Carl Jung (1875–1961) used the axiom as a metaphor for the process of individuation. One is unconscious wholeness; two is the conflict of opposites;...
without the axiom of choice) is still the best-known and most studied. Set theory is commonly employed as a foundational system for the whole of mathematics...
(if it existed) replaces the free variable. Hence any axiom with sets can be replaced by an axiom schema with monadic atomic subformulae. M8 and M8' are...
axiom schema containing a separate axiom for each possible predicate. The article Peano axioms contains further discussion of this issue. The axiom of...
because it is the fifth postulate in Euclid's Elements, is a distinctive axiom in Euclidean geometry. It states that, in two-dimensional geometry: If a...
This condition, called the T0 condition, is the weakest of the separation axioms. Nearly all topological spaces normally studied in mathematics are T0 spaces...
Positive Introspection Axiom, also known as the KK Axiom, says specifically that agents know that they know what they know. This axiom may seem less obvious...
In mathematics, the axiom of dependent choice, denoted by D C {\displaystyle {\mathsf {DC}}} , is a weak form of the axiom of choice ( A C {\displaystyle...
Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these...
The axiom of reducibility was introduced by Bertrand Russell in the early 20th century as part of his ramified theory of types. Russell devised and introduced...
In mathematical physics, the Wightman axioms (also called Gårding–Wightman axioms), named after Arthur Wightman, are an attempt at a mathematically rigorous...
numbers – Axiom(s) of Set Theory See § Emergence as a term Any Cauchy sequence in the Reals converges, Mendelson (2008, p. x) says: "The whole fantastic...
revealed the existence of non-Desarguesian planes, examples to show that the axioms of incidence can be modelled (in two dimensions only) by structures not...
writes that the first axiom is so clear that it requires no proof if only the idea of cause is understood. Example for the axiom: if a baseball is moving...
In mathematics, Smale's axiom A defines a class of dynamical systems which have been extensively studied and whose dynamics is relatively well understood...
logic, namely the axiom of infinity, the axiom of choice, and the axiom of reducibility. Since the first two were existential axioms, Russell phrased mathematical...
some thinkers, there are three axioms of environmental humanities: The axiom of submission to ecosystem laws; The axiom of ecological kinship, which situates...
on the set called multiplication that obeys the group axioms. The axiom of choice is an axiom of ZFC set theory which in one form states that every set...
sets, although there are some theorems that cannot be proven in common axiom systems for set theory. Contemporary work in the foundations of mathematics...
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