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Categoricity results for L∞κ

1988
*
Annals of Pure and Applied Logic
*

The

doi:10.1016/0168-0072(88)90049-8
fatcat:jwgtlrfd3bdxrpsingu4llg5x4
*L*"-theory of the pee algebras on K generators iis*categorical*in K*for*some tegdar non-weakly wmpact cardinal iff*for*all regular non-weakly compact K, the*L*"-theory of the jiee dgzbra on K generatom ... ig*categorical*in K. ... Section 4 is concerned with upward*categoric*@*results*. We consider varieties in a countable laquage where every*L*,-free algebra of cardinal@ ml is free. ...##
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Performance Evaluations of κ-Approximate Modal Haplotype Type Algorithms for Clustering Categorical Data

2015
*
Research Journal of Information Technology
*

These

doi:10.3923/rjit.2015.112.120
fatcat:kyfgwlcqxnh5fort5oeuvspvae
*results*present a new and significant benchmark, indicating that*κ*-AMH-type algorithms can be generalized*for*any*categorical*data. ... The effectiveness of the performance of*κ*-Approximate Modal Haplotype (*κ*-AMH)-type algorithms*for*clustering Y-short tandem repeats (Y-STR) of*categorical*data has been demonstrated previously. ... We would like to thank IRMI and UiTM*for*their support with this research. We also extend our gratitude to those who have contributed toward the completion of this study. ...##
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A short proof of Shelah's eventual categoricity conjecture for AEC's with interpolation, under GCH
[article]

2020
*
arXiv
*
pre-print

amalgamation which is a necessary and sufficient condition

arXiv:1909.13713v3
fatcat:quhdhjmjgjgspnavs64zqempdu
*for*an AEC*categorical*in a high enough cardinal to satisfy eventual*categoricity*. ... We provide a short proof of Shelah's eventual*categoricity*conjecture, assuming the Generalized Continuum Hypothesis (GCH),*for*abstract elementary classes (AEC's) with interpolation, a strengthening of ... Our*result*follows taking µ 0 to be the maximum of the Hanf numbers*for**categoricity*and non-*categoricity*. ...##
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Tameness from Large Cardinal Axioms
[article]

2014
*
arXiv
*
pre-print

We do so by showing that every AEC with LS(K) below a strongly compact cardinal

arXiv:1303.0550v4
fatcat:3bi32i46azcupnkmgzybth54ua
*κ*is <*κ*tame and applying the*categoricity*transfer of Grossberg and VanDieren. ... These techniques also apply to measurable and weakly compact cardinals and we prove similar tameness*results*under those hypotheses. ... A second*result*is that ( * ) −*κ**for**κ*regular and not weakly compact implies V =*L*. ...##
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ASSESSING SOME ESTIMATION CRITERIA OF MEASUREMENT ERROR FOR CATEGORICAL DATA

2017
*
International Journal of Applied Mathematics
*

Furthermore, based on the simulation

doi:10.12732/ijam.v30i2.1
fatcat:yooqzahc7bhhhllwggay5cgode
*results*, the standard error of the criteria is compared and the proper criterion is proposed*for*each of the cases of*categorical*data. ... In the previous investigations, modeling of measurement error*for*continues and*categorical*data is studied. ... In Table 1 , the effect of number of categories is computed*for*Cohen's kappa (*κ*), linear weighted kappa (*κ**L*W ) and quadratic weighted kappa (*κ*Q W ) criteria. ...##
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TAMENESS FROM LARGE CARDINAL AXIOMS

2014
*
Journal of Symbolic Logic (JSL)
*

We show that Shelah's Eventual

doi:10.1017/jsl.2014.30
fatcat:5jp5zfxz5nebpl73wdgy7kbbmi
*Categoricity*Conjecture*for*successors follows from the existence of class many strongly compact cardinals. ... We do so by showing that every AEC with LS(K) below a strongly compact cardinal*κ*is <*κ*-tame and applying the*categoricity*transfer of Grossberg and VanDieren [11]. ... A second*result*is that ( * ) −*κ**for**κ*regular and not weakly compact implies V =*L*. ...##
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A survey on tame abstract elementary classes
[article]

2016
*
arXiv
*
pre-print

We survey these developments using the following

arXiv:1512.00060v4
fatcat:7ll7eum7qveonlh7s7d3x7itfy
*result*(due to the second author) as our guiding thread: Theorem If a universal class is*categorical*in cardinals of arbitrarily high cofinality, then it ... is*categorical*on a tail of cardinals. ... These*results*can be strengthened in various ways. First, they apply also to AECs that are explicitly axiomatized in*L**κ*,ω . ...##
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A proof of Shelah's eventual categoricity conjecture and an extension to accessible categories with directed colimits
[article]

2022
*
arXiv
*
pre-print

Then, if 𝕋 is a ℒ_

arXiv:1906.09169v7
fatcat:e7ecwzoer5dnnd552jqjtcsbjm
*κ*, θ theory whose models have directed colimits and it is λ-*categorical**for*some λ≥μ in S, then it is λ'-*categorical**for*every λ' ≥μ in S; moreover, we also exhibit an example that shows ... When considering cardinalities of models of infinitary theories 𝕋 of ℒ_*κ*, θ that axiomatize 𝒦, the*result*implies, under SCH, the following infinitary version of Morley's*categoricity*theorem: let S ... This means that our eventual*categoricity**result**for*accessible categories with directed colimits is really a direct generalization of the same*result**for*AEC's. ...##
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Categoricity and infinitary logics
[article]

2015
*
arXiv
*
pre-print

We point out a gap in Shelah's proof of the following

arXiv:1508.03316v2
fatcat:xgak7mwpmjhqjfet236z7g5bd4
*result*: Claim Let K be an abstract elementary class*categorical*in unboundedly many cardinals. ... Let K be an abstract elementary class*categorical*in unboundedly many cardinals. ... If K is*categorical*in a λ > 2*κ*with cf(λ) >*κ*, then there exists a complete φ ∈*L*(2*κ*) + ,*κ*+ such that K ≥λ = (Mod(φ)) ≥λ and*for*M, N ∈ K ≥λ , M ≤ N if and only if M*L*∞,*κ*+ N. Definition 2.5. ...##
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Shelah's Categoricity Conjecture from a successor for Tame Abstract Elementary Classes
[article]

2005
*
arXiv
*
pre-print

This is an improvment of a Theorem of Makkai and Shelah ([Sh285] who used a strongly compact cardinal

arXiv:math/0509387v2
fatcat:ky5nwoezffdcjj3prdboowmfnu
*for*the same conclusion) and Shelah's downward*categoricity*theorem*for*AECs with amalgamation (from ... MAIN COROLLARY: (ZFC) If K is*categorical*in a successor cardinal bigger than _(2^μ)^+ then K is*categorical*in all cardinals greater than _(2^μ)^+. ... We now construct N 0 i , N 1 i ∈ K*κ*| i <*κ*+ satisfying the following: (1) N 0 0 = N (2) N*ℓ*i K N*ℓ**for**ℓ*= 0, 1 (3) the sequences N 0 i | i <*κ*+ and N 1 i | i <*κ*+ are both ≺ K - increasing and continuous ...##
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Some results on permutation group isomorphism and categoricity

2002
*
Journal of Symbolic Logic (JSL)
*

We extend Morley's Theorem to show that if a theory is

doi:10.2178/jsl/1190150138
fatcat:et5p2rcgljb5va7ojt6dey2baa
*κ*-p-*categorical**for*some uncountable cardinal*κ*, it is uncountably*categorical*. ... We then discuss ω-p-*categoricity*and provide examples to show that similar extensions*for*the Baldwin-Lachlan and Lachlan Theorems are not possible. ...*For**l*∈*κ*ω e , let ht(*l*) (the height of*l*) be the least value of n such that*for*all m ≥ n,*l*(m) = e. The important fact needed about*κ*ω e is the following: Proposition 2.2. ...##
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Shelah's categoricity conjecture from a successor for tame abstract elementary classes

2006
*
Journal of Symbolic Logic (JSL)
*

Letλ ≥ Max{χ, LS(K+}.If K is

doi:10.2178/jsl/1146620158
fatcat:7rm3fisf4zbkbbipa3o4gwyijy
*categorical*in λ and λ+, then K is*categorical*in λ++.Combining this theorem with some*results*from [37]. we derive a form of Shelah's*Categoricity*Conjecture*for*tame abstract ... Letμ0≔ Hanf(K).Ifand K is*categorical*in somethen K is*categorical*in μ*for*allμ. ... Given a countable language*L*and T a theory in*L*ω 1 ,ω , if Mod(T ) is*categorical*in λ*for*some λ > ω 1 , 1 then Mod(T ) is*categorical*in χ*for*every χ ≥ ω 1 . ...##
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Selective Revision by Deductive Argumentation
[chapter]

2012
*
Lecture Notes in Computer Science
*

By making use of previous

doi:10.1007/978-3-642-29184-5_10
fatcat:iprub7cxa5emloibnoepkqtedy
*results*on selective revision we prove that our revision operator satisfies several desirable properties. ... Herein, selective revision uses a two step approach, first applying a transformation function to decide if and which part of the new information shall be accepted, and second, incorporating the*result*... Φ | ∼*κ*,γ ¬α}*for*every Φ ⊆*L*(At). ...##
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Categoricity of theories in L_kappa^* omega, when kappa^* is a measurable cardinal. Part II
[article]

1996
*
arXiv
*
pre-print

We continue the work of [KlSh:362] and prove that

arXiv:math/9604241v1
fatcat:pamtrnoyujg2rnsuewi3j7eufa
*for*lambda successor, a lambda-*categorical*theory T in L_kappa^*, omega is mu-*categorical**for*every mu, mu <= lambda which is above the (2^LS(T))^+-beth ... We use the*results*obtained therein to advance our knowledge of the*categoricity*spectrum of theories in*L**κ** ,ω , when*κ** is a measurable cardinal. ... The notation follows [KlSh 362], except in two important details: we reserve*κ***for*the fixed measurable cardinal and T*for*the fixed λ-*categorical*theory in*L**κ** ,ω in a given vocabulary*L*.*κ*is any ...##
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Approximate Categoricity in Continuous Logic
[article]

2020
*
arXiv
*
pre-print

We also make progress towards an analog of Morley's theorem

arXiv:2011.00589v1
fatcat:dgckt3hbvrhxtaysqa36boqjv4
*for*inseparable approximate*categoricity*, showing that if there is some uncountable cardinal*κ*such that every model of size*κ*is 'approximately ... saturated,' in the appropriate sense, then the same is true*for*all uncountable cardinalities. ... The*results*are summarized in the Table 1 , where '*κ*∈ {ω, ω 1 }' means*κ*-*categorical*, 'Lip-*κ*' means Lip-*κ*-*categorical*and not*κ*-*categorical*, 'GH-*κ*' means GH-*κ*-*categorical*and not Lip-*κ*-*categorical*, and ...
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