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By using combinatorial properties of stationary sets, we give a simple proof of some generalization of Silver’s Theorem i.e. if κ is an uncountable regular cardinal such that אκ is a singular strong limit cardinal, then the following hold. (1). If {α < κ : א<κ α ≤ אα·2} is stationary, then 2אκ ≤ אκ·2. (2). If {α < κ : א<κ α ≤ אα+γ}, where 0 < γ < κ, is… (More)

- Pimpen Vejjajiva, Supakun Panasawatwong
- Notre Dame Journal of Formal Logic
- 2014

- Pimpen Vejjajiva
- Math. Log. Q.
- 2013

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… (More)

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