A cardinal λ is called ω-inaccessible if for all μ < λ we have μ < λ. We show that for every ω-inaccessible cardinal λ there is a CCC (hence cardinality and cofinality preserving) forcing that adds a hereditarily Lindelöf regular space of density λ. This extends an analogous earlier result of ours that only worked for regular λ. In [1] we have shown that for any cardinal λ a natural CCC forcing...

The theory of hereditarily finite sets is formalised, following the development of Świerczkowski [2]. An HF set is a finite collection of other HF sets; they enjoy an induction principle and satisfy all the axioms of ZF set theory apart from the axiom of infinity, which is negated. All constructions that are possible in ZF set theory (Cartesian products, disjoint sums, natural numbers, function...

In order to deene models of simply typed functional programming languages being closer to the operational semantics of these languages, the notions of sequentiality, stability and seriality were introduced. These works originated from the deenability problem for PCF, posed in Sco72], and the full abstraction problem for PCF, raised in Plo77]. The presented computation model, forming the class o...

We construct, assuming Jensen’s principle ♦, a one-dimensional locally connected hereditarily separable continuum without convergent sequences.

We prove for a large class of fields $F$ that every proper finite extension $F_{pyth}$, the pythagorean closure $F$, is not field. This contains number and are finitely generated transcendence degree at least one over some subfield $F$.

We show that a topological space is hereditarily irresolvable if and only if it is Hausdorff-reducible. We construct a compact irreducible T1-space and a connected Hausdorff space, each of which is strongly irresolvable. Furthermore, we show that the three notions of scattered, Hausdorff-reducible, and hereditarily irresolvable coincide for a large class of spaces, including metric, locally com...