categoricity造句

• It states that there should be a Hanf number for categoricity:
• Many conditions on a theory are equivalent to the property of omega-categoricity.
• Zermelo published a second-order axiomatization in 1930 and proved several categoricity results in that context.
• In 1959 he contributed an independent proof of several equivalent conditions to omega-categoricity, an important concept in model theory.
• Classification theory started with Morley's categoricity theorem, so it is natural to ask whether a similar result holds in AECs.
• Shelah also has several stronger conjectures : The threshold cardinal for categoricity is the Hanf number of psedo elemtary classes in a language of cardinality LS ( K ).
• Morley rank and strongly minimal structures are key tools in the proof of Morley's categoricity theorem and in the larger area of stability theory ( model theory ).
• He axiomatised these fields and, using Shelah on categoricity in infinitary logics, proved that this theory of " pseudo-exponentiation " has a unique model in each uncountable cardinal.
• By invalidating this premise, it proved that acceptance of the Axiom of categoricity is not a requirement but rather an idealistic option that may or may not be useful to a study.
• Such a metatheory is simply inadequate wrt the question you are discussing, it is meaningless to ask whether it proves categoricity of second-order arithmetic when it cannot even formulate it.
• In other words, he observed that, in all the cases he could think of, ?-categoricity at any one uncountable cardinal implied ?-categoricity at all other uncountable cardinals.
• In other words, he observed that, in all the cases he could think of, ?-categoricity at any one uncountable cardinal implied ?-categoricity at all other uncountable cardinals.
• I am fairly confident that categoricity of second-order arithmetic is provable in any reasonable metatheory where it is expressible .  J . 17 : 11, 23 October 2009 ( UTC)
• For example, when I proposed to interpret the second-order PA in General set theory, I was told, that in this case we could not prove its categoricity ( and consistency ).
• An axiomatic system for which every model is isomorphic to another is called "'categorial "'( sometimes categorical ), and the property of categoriality ( categoricity ) ensures the completeness of a system.
• By gathering variable data and analyzing it, he proved that the inconsistencies were indeed manageable, resisting the Axiom of categoricity's premise that the data be abstracted from social contexts in order to make it coherent and manageable.
• More specifically when the class is in a countable lenguage and axiomaziable by an L _ { \ omega _ 1, \ omega } sentence the threshold number for categoricity is \ beth _ { \ omega _ 1 }.
• Morley's categoricity theorem, proved by Michael D . Morley ( 1965 ), states that if a first-order theory in a countable language is categorical in some uncountable cardinality, i . e . all models of this cardinality are isomorphic, then it is categorical in all uncountable cardinalities.
• When interpreted as a proof within a first-order set theory, such as ZFC, Dedekind's categoricity proof for PA shows that each model of set theory has a unique model of the Peano axioms, up to isomorphism, that embeds as an initial segment of all other models of PA contained within that model of set theory.