We present a generalisation to ω2 of Baumgartner’s forcing for adding a CUB subset of ω1 with finite conditions. The following well-known result appears in Baumgartner, Harrington, Kleinberg [2]. For… (More)

There are many different ways to extend the axioms of ZFC. One way is to adjoin the axiom V = L, asserting that every set is constructible. This axiom has many attractive consequences, such as the… (More)

In this article we present a reformulation of the ne structure theory from Jensen 72] based on his theory for K and introduce the Fine Structure Principle, which captures its essential content. We… (More)

In this article we study the strength of Σ 1 3 absoluteness (with real parameters) in various types of generic extensions, correcting and improving some results from [2]. We shall also make some… (More)

The method of forcing has had great success in demonstrating the relative consistency and independence of set-theoretic problems with respect to the traditional ZFC axioms, or to extensions of these… (More)

Assume V = L. Let k be a regular cardinal and for X Qk let a(X) denote the least ordinal a such that ¿„[A"] is admissible. In this paper we characterize those ordinals of the form <x{X) using forcing… (More)

We give a model theoretic proof that if there is a counterexample to Vaught’s conjecture there is a counterexample such that every model of cardinality א1 is maximal (strengthening a result of… (More)