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Categoricity results for L∞κ

Paul C. Eklof, Alan H. Mekler
1988 Annals of Pure and Applied Logic  
The 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.  ... 
doi:10.1016/0168-0072(88)90049-8 fatcat:jwgtlrfd3bdxrpsingu4llg5x4

Performance Evaluations of κ-Approximate Modal Haplotype Type Algorithms for Clustering Categorical Data

Ali Seman, Azizian Mohd Sapawi, Mohd Zaki Salleh
2015 Research Journal of Information Technology  
These 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.  ... 
doi:10.3923/rjit.2015.112.120 fatcat:kyfgwlcqxnh5fort5oeuvspvae

A short proof of Shelah's eventual categoricity conjecture for AEC's with interpolation, under GCH [article]

Christian Espíndola
2020 arXiv   pre-print
amalgamation which is a necessary and sufficient condition 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.  ... 
arXiv:1909.13713v3 fatcat:quhdhjmjgjgspnavs64zqempdu

Tameness from Large Cardinal Axioms [article]

Will Boney
2014 arXiv   pre-print
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.  ...  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.  ... 
arXiv:1303.0550v4 fatcat:3bi32i46azcupnkmgzybth54ua


R. Alimohammadi
2017 International Journal of Applied Mathematics  
Furthermore, based on the simulation 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.  ... 
doi:10.12732/ijam.v30i2.1 fatcat:yooqzahc7bhhhllwggay5cgode


2014 Journal of Symbolic Logic (JSL)  
We show that Shelah's Eventual 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 &lt; 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.  ... 
doi:10.1017/jsl.2014.30 fatcat:5jp5zfxz5nebpl73wdgy7kbbmi

A survey on tame abstract elementary classes [article]

Will Boney, Sebastien Vasey
2016 arXiv   pre-print
We survey these developments using the following 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 .  ... 
arXiv:1512.00060v4 fatcat:7ll7eum7qveonlh7s7d3x7itfy

A proof of Shelah's eventual categoricity conjecture and an extension to accessible categories with directed colimits [article]

Christian Espíndola
2022 arXiv   pre-print
Then, if 𝕋 is a ℒ_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.  ... 
arXiv:1906.09169v7 fatcat:e7ecwzoer5dnnd552jqjtcsbjm

Categoricity and infinitary logics [article]

Will Boney, Sebastien Vasey
2015 arXiv   pre-print
We point out a gap in Shelah's proof of the following 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.  ... 
arXiv:1508.03316v2 fatcat:xgak7mwpmjhqjfet236z7g5bd4

Shelah's Categoricity Conjecture from a successor for Tame Abstract Elementary Classes [article]

Rami Grossberg, Monica VanDieren
2005 arXiv   pre-print
This is an improvment of a Theorem of Makkai and Shelah ([Sh285] who used a strongly compact cardinal 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 i K N for = 0, 1 (3) the sequences N 0 i | i < κ + and N 1 i | i < κ + are both ≺ K - increasing and continuous  ... 
arXiv:math/0509387v2 fatcat:ky5nwoezffdcjj3prdboowmfnu

Some results on permutation group isomorphism and categoricity

Anand Pillay, Mark D. Schlatter
2002 Journal of Symbolic Logic (JSL)  
We extend Morley's Theorem to show that if a theory is 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 lκ 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.  ... 
doi:10.2178/jsl/1190150138 fatcat:et5p2rcgljb5va7ojt6dey2baa

Shelah's categoricity conjecture from a successor for tame abstract elementary classes

Rami Grossberg, Monica Vandieren
2006 Journal of Symbolic Logic (JSL)  
Letλ ≥ Max{χ, LS(K+}.If K is 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 .  ... 
doi:10.2178/jsl/1146620158 fatcat:7rm3fisf4zbkbbipa3o4gwyijy

Selective Revision by Deductive Argumentation [chapter]

Patrick Krümpelmann, Matthias Thimm, Marcelo A. Falappa, Alejandro J. García, Gabriele Kern-Isberner, Guillermo R. Simari
2012 Lecture Notes in Computer Science  
By making use of previous 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).  ... 
doi:10.1007/978-3-642-29184-5_10 fatcat:iprub7cxa5emloibnoepkqtedy

Categoricity of theories in L_kappa^* omega, when kappa^* is a measurable cardinal. Part II [article]

Saharon Shelah
1996 arXiv   pre-print
We continue the work of [KlSh:362] and prove that 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  ... 
arXiv:math/9604241v1 fatcat:pamtrnoyujg2rnsuewi3j7eufa

Approximate Categoricity in Continuous Logic [article]

James Hanson
2020 arXiv   pre-print
We also make progress towards an analog of Morley's theorem 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  ... 
arXiv:2011.00589v1 fatcat:dgckt3hbvrhxtaysqa36boqjv4
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