Advances in Cardinal Arithmetic Sh420
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چکیده
I thank Alice Leonhardt for typing (and retyping) the manuscript so nicely and accurately.
منابع مشابه
Some remarks on cardinal arithmetic without choice
One important consequence of the Axiom of Choice is the absorption law of cardinal arithmetic. It states that for any cardinals m and n, if m 6 n and n is infinite, then m+ n = n and if m 6= 0, m · n = n. In this paper, we investigate some conditions that make this property hold as well as an instance when such a property cannot be proved in the absence of the Axiom of Choice. We further find s...
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Fairly deep results of Zermelo-Frænkel (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 result required developing theories of orders, order-isomorphisms, order types, ordinal arithmetic, cardinals, e...
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Part 1 Cardinality of Sets 2 1. Our Purpose 2 2. Introduction 2 3. Notation 3 4. Basic Operations 3 5. Notation and definitions for classes of cardinal numbers 3 6. Basic properties of Cardinal Arithmetic 5 7. General Arithmetic Properties Of Transfinite Cardinals 5 7.1. Useful Special Cases 5 7.2. General Cases 5 8. Specific Arithmetic Relations 6 8.1. Cases involving א0 6 8.2. Cases involving...
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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. Even elementary questions about the basic arithmetical operations of exponentiation in the context ...
متن کاملCardinal Arithmetic for Skeptics
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. Even elementary questions about the basic arithmetical operations of exponentiation in the context ...
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تاریخ انتشار 2011