Office: 510, Post-Doc, corridoio BC
Phone: (+39) 049 827 1461
E-mail: basilio.at.math.dot.unipd.dot.it
Stay: from 01/09/2014 to 31/08/2015
Older website: http://www.math.lmu.de/~karadais/
Interests: Higher-type computability theory, Denotational semantics of programming languages, Constructive domain theory
Working with: Giovanni Sambin, Francesco Ciraulo, Milly Maietti
Work
- Normal forms and linearity over nonflat domains (submitted)
UNIPD 2015
Outline (talk)
UNIPD 04.02.2015
Slides (talk)
Bridges between financial and constructive mathematics 2015
- Implicit atomicity and finite density for nonflat domains (preprint)
LMU 2013
- Atomicity, coherence of information, and point-free structures (to appear)
LMU 2013
- Towards an arithmetic for partial computable functionals (phd thesis)
LMU 2013
Outline of the defense talk (talk)
LMU 12.08.2013
- Atomicity in non-atomic information systems (talk)
Foundation of mathematics for computer-aided formalization 2013
- Recognizing tokens in a finitary algebra (unpublished) (a theorem of Schröter, Gerneth & Hall)
LMU 2012
Note. The main observation in the text (Proposition, p. 3) is Theorem 2.3, part III, in P. M. Cohn's Universal algebra (1981), or Theorem 1 in Chapter IV, Section 1, in C. Rosenbloom's Elements of mathematical logic (1950).
Following the references in these textbooks, we find that the idea was already known in the early 30's. Karl Menger ("Eine elementare Bemerkung über die Struktur logischer Formeln", Ergebnisse eines mathematischen Kolloquiums, vol. 3, 1930/31, pp. 22–3) had it in the context of Łukasiewicz' prefix notation for the propositional calculus (also called "polish notation"), for the case of an alphabet with unary and binary constructors—the intuition stemming from the negation and the logical connectives respectively. He thus derived a necessary and sufficient condition for a string to be a well-formed formula. Rosenbloom informs us that the same observation was independently made by Kazimierz Ajdukiewicz as well.
Karl Schröter ("Axiomatisierung der Fregeschen Aussagenkalküle", Forschungen zur Logik und zur Grundlegung der exakten Wissenschaften, neue Folge, Heft 8, 1943) discusses the case of arbitrary arities, as does Dal Charles Gerneth later, independently ("Generalization of Menger's result on the structure of logical formulas", Bulletin of the American Mathematical Society, vol. 54, 1948, pp. 803–804). Rosenbloom again informs us that Philip Hall, also independently, had made the same general observation; indeed, Hall talks about this "paradox of the pointlessness of punctuation" several years later, in his fairly well-known address to the London Mathematical Society ("Some word-problems", Journal of the London Mathematical Society, second series, vol. 33, 1958, pp. 482–496).
One can only admire the wonderful robustness of mathematical activity...
Many-many thanks to Magnus Steinby, who kindly referred me to Cohn's book seven months ago in January 2014. I've been meaning to update the text and pay the necessary dues all this time, but...
- Towards a formal theory of computability (preprint), with S. Huber and H. Schwichtenberg
Ways οf proof theory (Pohler's festschrift), 2010
A case study (talk)
Arbeitstagung Βern–München 2010
- Plotkin definability theorem for atomic-coherent information systems (talk)
Computability in Europe 2008
- Normal form of finite algebraic approximations (talk)
Seminar on proof theory WS 2006/7
- Elaborating on Ishihara's 'WKL implies FAN' (talk)
EST training workshop 2005
Teaching
Links
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A talk by Simon Peyton Jones on writing research, which interestingly (and eerily) feels like King's "On Writing" boiled down to some slides—plus some research-specific common sense of course (the kind of common sense though that is rarely spoken out loud in the academia these days). Terence Tao also has interesting things to say, as well as has gathered several links on the subject, here.
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There was an old greek guy (really old, we call these "ancient" by now), Antisthenes, who's said to have held that education begins with the pondering on words. In this spirit, Robert Harper asks, "What, if anything, is a declarative language?"
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A talk at the Institute for Advanced Study in Princeton, by Andrej Bauer (see below for his blog), on constructive mathematics for old-school mathematicians.
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Here's a nice note on the axiom of choice by Thomas Forster (via Peter Smith's guide, see below).
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Peter Smith has been compiling a diy guide on learning logic in his very british blog. He updates it here.
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Albert Bartlett's lecture on Arithmetic, Population, and Energy, an interesting as well as a cozy watch.
- Stephen Strogatz' New
York Times Blog
- Mathematics and Computation,
Andrej Bauer's very interesting
blog
- Answers to frequently
asked questions about Constructive Mathematics, by Douglas Bridges
- Of pi's and fetishists: Michael
Hartl takes on \(\pi\) versus \(2\pi\).
- Richard Elwes' Simple City
- "Math is just a serious game" (sic)
- PhD Comics,
the must link on every Ph.D.'s webpage (even when the Ph.D. is over)
Last modified: 20.07.2015