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On the consistency strength of 'Accessible' Jonsson Cardinals and of the Weak Chang Conjecture

Hans-Dieter Donder, Peter Koepke
1983 Annals of Pure and Applied Logic  
For A = P+ a successor cardinal we consider the weak Chang Conjecture, WCC(A), which is a consequence of the Chang transfer property (A+, A) j (A, p). III.  ...  Assume that A is a Jonsson cardinal which is 'accessible' in the sense that at least one of (l)-(4) holds: (1) A is a successor cardinal; (2) A = oE and 6 <A ; (3) A is singular of uncountable cofinality  ...  Theorem B contrasts with results of Silver and the first author about the consistency strength of the Chang Conjecture (02, wl) + (ol, wO).  ... 
doi:10.1016/0168-0072(83)90020-9 fatcat:3hohxm6apjajbekcqogkusvm3m

Consistency strength of higher chang's conjecture, without CH

Sean D. Cox
2011 Archive for Mathematical Logic  
We prove that (ω 3 , ω 2 ) (ω 2 , ω 1 ) implies there is an inner model with a weak repeat measure.  ...  Jónsson cardinals and algebras are also closely related to Chang's Conjecture: Vickers and Welch [14] used covering arguments with the core model to show that K correctly computes successors of Jónsson  ...  (ω 2 , ω 1 ) (ω 1 , ω) is equiconsistent with an ω 1 -Erdös cardinal (see [3] ), but shifting the cardinals in the statement upward results in a stronger statement in terms of consistency strength.  ... 
doi:10.1007/s00153-011-0247-6 fatcat:f3spo4zhyjfndf7nxn2jz3olr4

LOCAL CLUB CONDENSATION AND L-LIKENESS

PETER HOLY, PHILIP WELCH, LIUZHEN WU
2015 Journal of Symbolic Logic (JSL)  
, CC(κ +) - Chang's Conjecture at κ + - is consistent with Local Club Condensation at κ +, both under suitable large cardinal consistency assumptions.  ...  We show that Local Club Condensation at κ + is consistent with ¬☐ κ whenever κ is regular and uncountable, generalizing and improving a result of the third author in [14], and that if κ ≥ ω 2 is regular  ...  In the extension, Local Club Condensation holds and the supremum of the measurable cardinals is accessible and Jónsson (see [11] ).  ... 
doi:10.1017/jsl.2015.6 fatcat:5qz6xod7mjednijsmjlnrpktya

Singular Cardinals [chapter]

Menachem Kojman
2012 Handbook of the History of Logic  
This was the missing part for completing the work of Gitik and Mitchell on the consistency strength of the Singular Cardinal Hypothesis.  ...  One can say that some chaos is displayed in the behavior of the binomial, but only for a "small" part of the universe, and at a high consistency-strength cost.  ...  ., 15 almost free group, 23 Axiom of Choice, 6  ... 
doi:10.1016/b978-0-444-51621-3.50007-4 fatcat:fr3pdoy3nbdn5pc4pz52reng24

Some applications of short core models

Peter Koepke
1988 Annals of Pure and Applied Logic  
The covering and condensation properties of short core models were applied to obtain information on the consistency strengths of certain instances of Chang's conjecture, the Mnsson property and the free  ...  We consider instances of Chang's conjecture, 'accessible' J&son cardinals, the free subset property for small cardinals, a canonixation property of o" and a non-closure property of elementary embeddings  ...  I(1 Theorem 3.118 there exists U'>, U ]r(' with mindom(U'\ contradicts the de6nition of Ucan. Cl 5. on J&son cardinals see Chang-Keisler [1,?.3.2].  ... 
doi:10.1016/0168-0072(88)90026-7 fatcat:h6k4bh6eebbppiqmnexyy7vvlq

Large Cardinals with Forcing [chapter]

Akihiro Kanamori
2012 Handbook of the History of Logic  
As in many situations, ω 2 typified an accessible cardinal in the investigation of the consistency strength of stationary set reflection, as described above, but with ω 2 paradigmatic of successors of  ...  [Dales and Woodin, 1987] ), built on by Solovay, on the consistency of Kaplansky's Conjecture (Is every homomorphism on the Banach algebra of continuous functions on the unit interval continuous?)  ... 
doi:10.1016/b978-0-444-51621-3.50004-9 fatcat:rxofgx3z6nelvlyhmdybzlox6e

Inner Models for Large Cardinals [chapter]

William J. Mitchell
2012 Handbook of the History of Logic  
The concept of a measurable cardinal will serve as both a goal and a benchmark. 6 The first part of the story will largely concern the effect which the presence of a measurable cardinal has on the constructible  ...  One new idea leads to another, that to a third, and so on through a course of time until someone, with whom no one of these is original, combines all together, and produces what is justly called a new  ...  One of the results in this paper was 9 that if it is consistent that there is a supercompact cardinal, then it is consistent that the filter of nonstationary sets on ω 1 is saturated.  ... 
doi:10.1016/b978-0-444-51621-3.50005-0 fatcat:m3yjj6pueveizmlqy4dkfp5lju

COMBINATORIAL GEOMETRIES [chapter]

2011 Geometry, Perspective Drawing, and Mechanisms  
The use of powerful combinatorial tools such as the Erdös-Rado theorem on the one hand and the discovery that Chang's conjecture on two cardinal models for arbitrary first theories is independent of ZFC  ...  Then |S( M )| ≤ κ µ · µ = κ and we finish. 12.10 Lieberman [Lie, Lie09] obtains a variant on Theorem 12.10 considering weak tameness rather than tameness; notably, an appeal to the study of accessible  ...  In particular, by ( * ) for any s : ω → 2 the functions s and f (s) are E 0 -equivalent. We focus now on the stalks of the form G * a0,ai , G * a0,bt , H * ai,bt , i ≥ 1.  ... 
doi:10.1142/9789814343831_0002 fatcat:zinkt54wavd4ddp5rmv2g33rxy

Completeness-via-canonicity for coalgebraic logics [article]

Fredrik Dahlqvist
2015 arXiv   pre-print
We have chosen to investigate the possibility to generalize what is arguably one of the most successful methods to prove completeness results in 'classical' modal logic, namely completeness-via-canonicity  ...  This technique is particularly well-suited to a coalgebraic generalization because of its clean and abstract algebraic formalism.  ...  Let C be a λ-accessible category and let Acc λ be the subcategory of Set C consisting of λ-accessible functors. Acc λ is locally finitely presentable. Proof.  ... 
arXiv:1510.09095v1 fatcat:vzxyx4z4knh5pgwp3si4fvgc44

Weak bases of Boolean co-clones

Victor Lagerkvist
2014 Information Processing Letters  
We then proceed to study the computational complexity of two optimisation variants of the SAT(S) problem: the maximum ones problem over a Boolean constraint language S (MAX-ONES(S)) and the valued constraint  ...  For MAX-ONES(S) we use partial clone theory and prove that MAX-ONES({R = = = 1/3 }) is the easiest NPcomplete MAX-ONES(S) problem.  ...  Since the lattice of Boolean strong partial clones is of uncountably infinite cardinality, and the lattice of Boolean clones is of countably infinite cardinality, it follows that the cardinality of Int  ... 
doi:10.1016/j.ipl.2014.03.011 fatcat:4rhokivpgnaxrptedshzn2emji

Changing a Semantics: Opportunism or Courage? [chapter]

Hajnal Andréka, Johan van Benthem, Nick Bezhanishvili, István Németi
2014 Studies in Universal Logic  
This paper is dedicated to Leon Henkin, a deep logician who has changed the way we all work, while also being an always open, modest, and encouraging colleague and friend.  ...  The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic.  ...  of interpretation for our language, or its 'access' to the model.  ... 
doi:10.1007/978-3-319-09719-0_20 fatcat:vozrx72hn5etnkm3r65t7ejrum

On completions, neat embeddings and omittings types, yet again [article]

Tarek Sayed Ahmed
2013 arXiv   pre-print
Various connections between the notions of strong representability and complete representability are given in terms of neat embeddings.  ...  As a sample, we show that it T is an L_n theory and |T|=lambda, lambda a regular cardinal, if T admits elimination of quantifiers, then T omits < 2^λ many non isolated maximal types.  ...  Letx enumerate nodes(N s ) ∩ nodes(N t ) Ifx is short, then there are at most two nodes in the intersection and this case is similar to the cylindrifier move, she uses ρ s for the suffixes of the red.  ... 
arXiv:1307.1016v1 fatcat:wvhibz354fedjolfyikgcqdci4

On the finitizability problem in algebraic logic; recent results [article]

Tarek Sayed Ahmed
2013 arXiv   pre-print
This is a survey article in algebraic logic, where we take a magical tour from old concepts due to Henkin, Monk and Tarski like neat embeddings, to modern views and perspectives, culminating in the use  ...  of Erdos graphs in settling important questions in algebraic logic.  ...  Now twisting, originally, consists of starting from a complete atomic CA α A, selecting atoms a, b ∈ A and an ordinal k < α and then redefining c k on a and b by interchanging the action of c k on a and  ... 
arXiv:1302.1368v1 fatcat:bguykr2afvfajda4qskyr265ge

Papers read at the 25th Annual Meeting of the Psychonomic Society

1984 Bulletin of the Psychonomic Society  
Strengths and weaknesses of life episodes as mediators are discussed within a fivestage process model. 1:20-1:35 (140) Memory for Personal Events Occurring in Different Modalities. CHARLES P.  ...  Few children not using the cardinality rule forgot the final word used in counting, and most made some use of the cardinality rule after brief teaching. 11:35-11:50 (46) The Development of Picture-Word  ...  Champaign-"Ratios of differences" and "differences of differences" are consistent with the two instructed operations on a common ratio scale of "differences."  ... 
doi:10.3758/bf03333825 fatcat:ol36my642vbnnfloz4qqyp7i5m

Cylindric and polyadic algebras, new perspectives [article]

Tarek Sayed Ahmed
2013 arXiv   pre-print
This allows us to lift a plathora of deep results proved for finite dimensions to the infinite dimensional case, like the solution to problem 2.12 in Henkin Monk and Tarski part one, solved by Hirsch and  ...  One is fixed, the alledged result in the second is weakened.  ...  It is a both a completeness and a Robinson's joint consistency theorem, but not in the full strength as in the case of first order logic.  ... 
arXiv:1309.0681v1 fatcat:35vlva4kpvdd3cl6ihc4dkjl3y
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