منابع مشابه
Stationary reflection principles and two cardinal tree properties
We study consequences of stationary and semi-stationary set reflection. We show that the semi-stationary reflection principle implies the Singular Cardinal Hypothesis, the failure of weak square principle, etc. We also consider two cardinal tree properties introduced recently by Weiss and prove that they follow from stationary and semi-stationary set reflection augmented with a weak form of Mar...
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Assuming the existence of a Mahlo cardinal, we produce a generic extension of Gödel’s constructible universe L, in which the GCH holds and the transfer principles (א2,א0) → (א3,א1) and (א3,א1) → (א2,א0) fail simultaneously. The result answers a question of Silver from 1971. We also extend our result to higher gaps.
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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...
متن کاملCardinal Numbers
We present the choice function rule in the beginning of the article. In the main part of the article we formalize the base of cardinal theory. In the first section we introduce the concept of cardinal numbers and order relations between them. We present here Cantor-Bernstein theorem and other properties of order relation of cardinals. In the second section we show that every set has cardinal nu...
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ژورنال
عنوان ژورنال: JTCVS Techniques
سال: 2020
ISSN: 2666-2507
DOI: 10.1016/j.xjtc.2020.06.033