Basil A. KarádaisArbeitsgruppe Mathematische LogikMathematisches Institut der Universität München Email: karadais[at]math.lmu.de Tel: +49 (0)89 2180 4417 Sprechstunde: Nach Vereinbarung 

Teaching
 SS14: Programming and modeling
Functional programming in Haskell  WS13/14: Mathematical Logic
 SS13: Logic and Discrete Structures
A dry, uncommented Mathematica file for the exercise A93: LDS13A93.nb (45KB).  WS12/13: Single Variable Calculus
 SS12: Logic and Discrete Structures
 WS11/12: Analysis I for students of Computer Science and Statistics
 WS10/11: Geometry
 SS10: Mathematical Logic II
 WS09/10: Linear Algebra for students of Computer Science and Statistics
 SS09: Synthetic und analytic treatment of geometric problems
 WS08/09: Differential and Integral Calculus III
 SS08 Complex Analysis (Funktionentheorie) (ss08_ft.rar, 2.5MB)
 SS07: Mathematical Logic II (ss07_mlii.rar, 390KB)
 SS05: Linear Algebra II
Work
 Implicit atomicity and finite density for nonflat domains (work in progress)
L.M.U. 2013
 Atomicity, coherence of information, and pointfree structures (preprint)
L.M.U. 2013
 Towards an arithmetic for partial computable functionals (phd thesis)
L.M.U. 2013
Outline of the defense talk (talk)
L.M.U. 12.08.2013  Atomicity in nonatomic information systems (talk)
Foundation of mathematics for computeraided formalization 2013  Recognizing tokens in a finitary algebra (a theorem of Schröter, Gerneth & Hall)
L.M.U. 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 wellformed 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 wellknown address to the London Mathematical Society ("Some wordproblems", Journal of the London Mathematical Society, second series, vol. 33, 1958, pp. 482–496).
One can only admire the wonderful robustness of mathematical activity...
Manymany 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 Î¿f proof theory (Pohler's festschrift), 2010
A case study (talk)
Arbeitstagung Î’ern–MÃ¼nchen 2010  Plotkin definability theorem for atomiccoherent 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
Links
 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 researchspecific 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.
 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?"
 A talk at the Institute for Advanced Study in Princeton, by Andrej Bauer (see below for his blog), on constructive mathematics for oldschool mathematicians.
 Here's a nice note on the axiom of choice by Thomas Forster (via Peter Smith's guide, see below).
 Peter Smith has been compiling a diy guide on learning logic in his very british blog. He updates it here.
 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
And a bit more
 Suppose you're interested in the philosophy of mathematics; and there's this talk that you hear about, that contains the words "mathematical philosophy" in the title or abstract; now, if the guy who's giving the talk is a mathematician, he should certainly mean what he says, right? (of course...) so, you wouldn't attend  you're not interested in the mathematics of philosophy after all; if the guy (or the girl, let's not be american pee cee here) is a nonmathematician, even if he means to talk about the philosophy of mathematics, he obviously can't use the words right; so again, you shouldn't bother to attend. If you nevertheless do attend, then you should be decent enough not to complain afterwards.
 Among manymany things, this or this, in street german as I personally understand it, is what you would call "voll nazi". Now, if you're among the academia or pseudoacademia people who prefer to reserve the term for the hitler era, just call it "criminally arrogant" and let's stay friends, what d'you say?
 Shhhhit... — but still.
Last modified: 29.07.2014