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198
FURTHER CARDINAL ARITHMETIC
 ISRAEL JOURNAL OF MATHEMATICS 95 (1996), 61–114
, 1996
"... We continue the investigations in the author’s book on cardinal arithmetic, assuming some knowledge of it. We deal with the cofinality of (S≤ℵ0 (κ), ⊆) for κ real valued measurable (Section 3), densities of box products (Section 5,3), prove the equality cov(λ, λ, θ +, 2) = pp(λ) in more cases even ..."
Abstract

Cited by 41 (22 self)
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We continue the investigations in the author’s book on cardinal arithmetic, assuming some knowledge of it. We deal with the cofinality of (S≤ℵ0 (κ), ⊆) for κ real valued measurable (Section 3), densities of box products (Section 5,3), prove the equality cov(λ, λ, θ +, 2) = pp(λ) in more cases even
Forcing Axioms and Cardinal Arithmetic
, 2006
"... We survey some recent results on the impact of strong forcing axioms such as the Proper Forcing Axiom PFA and Martin’s Maximum MM on cardinal arithmetic. We concentrate on three combinatorial principles which follow from strong forcing axioms: stationary set reflection, Moore’s Mapping Reflection Pr ..."
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We survey some recent results on the impact of strong forcing axioms such as the Proper Forcing Axiom PFA and Martin’s Maximum MM on cardinal arithmetic. We concentrate on three combinatorial principles which follow from strong forcing axioms: stationary set reflection, Moore’s Mapping Reflection
Cardinal arithmetic for skeptics
 Bull. Amer. Math. Soc. New Series
, 1992
"... When modern set theory is applied to conventional mathematical problems, it has a disconcerting tendency to produce independence results rather than theorems in the usual sense. The resulting preoccupation with “consistency ” rather than “truth ” may be felt to give the subject an air of unreality. ..."
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Cited by 14 (4 self)
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. Even elementary questions about the basic arithmetical operations of exponentiation in the context of infinite cardinalities, like the value of 2 ℵ0, cannot be settled on the basis of the usual axioms of set theory (ZFC). Although much can be said in favor of such independence results, rather than
Cardinal Arithmetic in Weak Theories
, 2008
"... In this paper we develop the theory of cardinals in the theory COPY. This is the theory of two total, jointly injective binary predicates in a second order version, where we may quantify over binary relations. The only second order axioms of the theory are the axiom asserting the existence of an emp ..."
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consequence is that our development of cardinals is inherited by stronger theories like AS. We will show that the cardinals satisfy (at least) Robinson’s Arithmetic Q. A curious aspect of our approach is that we develop cardinal multiplication using neither recursion nor pairing, thus diverging both from
Extraresolvability and cardinal arithmetic
 COMMENT.MATH.UNIV.CAROLIN. 40,2 (1999)279–292
, 1999
"... Following Malykhin, we say that a space X is extraresolvable if X contains a family D of dense subsets such that D > ∆(X) and the intersection of every two elements of D is nowhere dense, where ∆(X) = min{U  : U is a nonempty open subset of X} is the dispersion character of X. We show that, ..."
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, for every cardinal κ, there is a compact extraresolvable space of size and dispersion character 2κ. In connection with some cardinal inequalities, we prove the equivalence of the following statements: 1) 2κ < 2κ, 2) (κ+)κ is extraresolvable and 3) A(κ+)κ is extraresolvable, where A(κ+) is the one
∗Keywords: Cardinal arithmetic, singular cardinals problem, pcf
, 1991
"... Abstract 3∗ We look at an old conjecture of A. Tarski on cardinal arithmetic and show that if a counterexample exists, then there exists one of length ω1 + ω. 1Supported partially by an NSF grant. I wish to express my gratitude to the Mathematical Institute of the Eidgenössische Technische Hochschul ..."
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Abstract 3∗ We look at an old conjecture of A. Tarski on cardinal arithmetic and show that if a counterexample exists, then there exists one of length ω1 + ω. 1Supported partially by an NSF grant. I wish to express my gratitude to the Mathematical Institute of the Eidgenössische Technische
Proper Forcing, Cardinal Arithmetic, and Uncountable . . .
"... In this paper I will communicate some new conse ..."
Mechanizing set theory: Cardinal arithmetic and the axiom of choice
 Journal of Automated Reasoning
, 1996
"... Abstract. Fairly deep results of ZermeloFrænkel (ZF) set theory have been mechanized using the proof assistant Isabelle. The results concern cardinal arithmetic and the Axiom of Choice (AC). A key result about cardinal multiplication is κ ⊗ κ = κ, where κ is any infinite cardinal. Proving this resu ..."
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Cited by 16 (9 self)
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Abstract. Fairly deep results of ZermeloFrænkel (ZF) set theory have been mechanized using the proof assistant Isabelle. The results concern cardinal arithmetic and the Axiom of Choice (AC). A key result about cardinal multiplication is κ ⊗ κ = κ, where κ is any infinite cardinal. Proving
CARDINAL ARITHMETIC IN THE STYLE OF Baron Von Münchhausen
, 2009
"... In this paper we show how to interpret Robinson’s Arithmetic Q and the theory R of Tarski, Mostowski and Robinson as theories of cardinals in very weak theories of relations over a domain. ..."
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In this paper we show how to interpret Robinson’s Arithmetic Q and the theory R of Tarski, Mostowski and Robinson as theories of cardinals in very weak theories of relations over a domain.
Results 1  10
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198