arXiv subjects

Gabriele Gullà

Publications and source records attributed to Gabriele Gullà.

4 recordsLinked to original sources

arXiv2024

A short survey around the pumping lemma for context-free languages

Following a seminar the present author gave to an Automata Theory course to computer science students, it will be presented, in a very synthetic and mostly selfcontained way, the principal properties of context free languages (CFL), with particular attention given to the Pumping Lemma (PL), and of grammars which generate them(CFG). We refer to Chomsky and Schutzenberger for the first works about it. What is known in literature as the Iteration Theorem here will be referred to as the Ogden's Lemma in a fully justified way. All definitions not strictly connected with the notion of context freeness will be omitted (we will give precise references for all of them). The symbology used is substantially the classical one, but we will replace some symbols to avoid confusion with those used in logic

cs.FL↗

arXiv2024

On a relation between $λ$-full well-ordered sets and weakly compact cardinals

We prove, via transfinite recursion, the existence, inside any linearly ordered set of appropriate regular cardinality $λ$, of a particular kind of well-ordered subsets characterized by the property of $λ$-fullness. Let $H$ be a set of regular cardinals: by using our results about well-ordered $λ$-full sets we show that if $\inf H$ is a weakly compact cardinal, then, for every LOTS $X$, $H$-compactness is equivalent to the nonexistence of gaps of types in $H$.

math.LO↗

arXiv2024

A synthetic overview on some known characterizations of Woodin cardinals

This brief survey comes from the slides of a seminar I gave to philosophy of mathematics students. I will present some different characterizations of Woodin cardinals, including the one obtained by Ernest Schimmerling in [6]. I will try to give to this paper the most self-contained possible structure, also by showing explicitly just the proofs usually leaved to the reader, and giving exact references for the others.

math.LO↗

arXiv2024

Some observations on a result by Bialinicki-Birula and Zelazko

We are interested in investigating some definitions and assumptions stated in [4], in particular the notions of measurability and atomicity that the two authors used in order to give a representation for multiplicative linear functionals (m.l.f. so on) over the cartesian product of algebras. We want to briefly analyze the result under other strong proper axioms with respect to ZF(C). Some little historical and notational remarks will be given.

math.LO↗