Search results: 1
We will learn about the axioms of ZF, the role of Foundation, ordinals and cardinals, cofinality and some basic results in cardinal arithmetic.
We will learn about the axiom of choice (the well ordering principle, Zorn's lemma) and other equivalents and consequences.
We will introduce the Levy hierarchy of formulas and talk about reflection and absoluteness.
Towards proving consistency results, we will talk about inner models and relativization. We will use von Neuman's hierarchy in order to prove the relative consistency of Foundation relative to ZF - Foundation. We will construct L and conclude that the continuum hypothesis and the axiom of choice are consistent relative to ZF.
We will learn about the axiom of choice (the well ordering principle, Zorn's lemma) and other equivalents and consequences.
We will introduce the Levy hierarchy of formulas and talk about reflection and absoluteness.
Towards proving consistency results, we will talk about inner models and relativization. We will use von Neuman's hierarchy in order to prove the relative consistency of Foundation relative to ZF - Foundation. We will construct L and conclude that the continuum hypothesis and the axiom of choice are consistent relative to ZF.
- Teacher: Yair Hayut