Set theory seminar -Forcing axioms and inner models II

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In this second talk I proved the equivalence of Bagaria’s, and Goldstern-Shelah’s formulation of the bounded forcing axiom for a poset ${\mathbb P}$ that preserves $\omega_1$ .

We presented several characterizations of club subsets of ${\mathcal P}_{\omega_1}(X)$ for $X$ uncountable. We then defined when a forcing notion is proper and provided some basic examples of proper forcings, namely ccc, $\sigma$ -closed forcings, and their products.

Go to next talk.
Go to the intermezzo for a discussion of consistency strengths.

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6 Responses to Set theory seminar -Forcing axioms and inner models II

Set theory seminar -Forcing axioms and inner models « Teaching page says:

October 25, 2008 at 2:18 pm

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Set theory seminar -Forcing axioms and inner models III « Teaching page says:

October 25, 2008 at 2:45 pm

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Set theory seminar -Forcing axioms and inner models -Intermezzo « Teaching page says:

October 25, 2008 at 3:13 pm

[…] Second talk, September 19, 2008. […]

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Set theory seminar -Forcing axioms and inner models | A kind of library says:

February 26, 2019 at 12:56 pm

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Set theory seminar -Forcing axioms and inner models -Intermezzo | A kind of library says:

February 26, 2019 at 1:46 pm

[…] Second talk, September 19, 2008. […]

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Set theory seminar -Forcing axioms and inner models III | A kind of library says:

February 26, 2019 at 2:24 pm

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