Related categories
Siblings:History/traditions: Mathematics
16 found
Search inside:
(import / add options)   Sort by:
  1. Dwight R. Bean (1976). Effective Coloration. Journal of Symbolic Logic 41 (2):469-480.
    We are concerned here with recursive function theory analogs of certain problems in chromatic graph theory. The motivating question for our work is: Does there exist a recursive (countably infinite) planar graph with no recursive 4-coloring? We obtain the following results: There is a 3-colorable, recursive planar graph which, for all k, has no recursive k-coloring; every decidable graph of genus p ≥ 0 has a recursive 2(χ(p) - 1)-coloring, where χ(p) is the least number of colors which will suffice (...)
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  2. Vieri Benci, Leon Horsten & Sylvia Wenmackers (2013). Non-Archimedean Probability. Milan Journal of Mathematics 81 (1):121-151.
    We propose an alternative approach to probability theory closely related to the framework of numerosity theory: non-Archimedean probability (NAP). In our approach, unlike in classical probability theory, all subsets of an infinite sample space are measurable and only the empty set gets assigned probability zero (in other words: the probability functions are regular). We use a non-Archimedean field as the range of the probability function. As a result, the property of countable additivity in Kolmogorov’s axiomatization of probability is replaced by (...)
    Remove from this list | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  3. Arthur W. Burks & Jesse B. Wright, Sequence Generators, Graphs, and Formal Languages.
    A sequence generator is a finite graph, more general than, but akin to, the usual state diagram associated with a finite automaton. The nodes of a sequence generator represent complete states, and each node is labeled with an input and an output state. An element of the behavior of a sequence generator is obtained by taking the input and output states along an infinite path of the graph.Sequence generators may be associated with formulas of the monadic predicate calculus, in which (...)
    Remove from this list |
    Translate to English
    | Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  4. Stanislas Dehaene, Véronique Izard, Pierre Pica & Elizabeth Spelke (2009). Response to Comment on "Log or Linear? Distinct Intuitions on the Number Scale in Western and Amazonian Indigene Cultures&Quot;. Science 323 (5910):38.
    The performance of the Mundurucu on the number-space task may exemplify a general competence for drawing analogies between space and other linear dimensions, but Mundurucu participants spontaneously chose number when other dimensions were available. Response placement may not reflect the subjective scale for numbers, but Cantlon et al.'s proposal of a linear scale with scalar variability requires additional hypotheses that are problematic.
    Remove from this list |
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  5. Anatolij Dvurečenskij & Jiří Janda (2013). On Bilinear Forms From the Point of View of Generalized Effect Algebras. Foundations of Physics 43 (9):1136-1152.
    We study positive bilinear forms on a Hilbert space which are not necessarily bounded nor induced by some positive operator. We show when different families of bilinear forms can be described as a generalized effect algebra. In addition, we present families which are or are not monotone downwards (Dedekind upwards) σ-complete generalized effect algebras.
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  6. Gérard G. Emch (2002). Mathematical Topics Between Classical and Quantum Mechanics. Studies in History and Philosophy of Science Part B 33 (1):148-150.
    Remove from this list | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  7. James Franklin (2006). Review of N. Wildberger, Divine Proportions: Rational Trigonometry to Universal. [REVIEW] Mathematical Intelligencer 28 (3):73-74.
    Reviews Wildberger's account of his rational trigonometry project, which argues for a simpler way of doing trigonometry that avoids irrationals.
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  8. James Franklin (1996). Proof in Mathematics: An Introduction. Quakers Hill Press.
    Why do students take the instruction "prove" in examinations to mean "go to the next question"? Because they have not been shown the simple techniques of how to do it. Mathematicians meanwhile generate a mystique of proof, as if it requires an inborn and unteachable genius. True, creating research-level proofs does require talent; but reading and understanding the proof that the square of an even number is even is within the capacity of most mortals.
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  9. James Franklin (1988). Homomorphisms Between Verma Modules in Characteristic P. Journal of Algebra 112:58-85.
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  10. K. Gödel (1931). Über Formal Unentscheidbare Sätze der Principia Mathematica Und Verwandter Systeme I. Monatshefte für Mathematik 38 (1):173--198.
    Remove from this list |
    Translate to English
    |
     
    My bibliography  
     
    Export citation  
  11. Harold T. Hodes (1988). Book Review. The Lambda-Calculus. H. P. Barendregt(. [REVIEW] Philosophical Review 97 (1):132-7.
    Remove from this list |
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  12. Harold T. Hodes (1982). Jumping to a Uniform Upper Bound. Proceedings of the American Mathematical Society 85 (4):600-602.
    A uniform upper bound on a class of Turing degrees is the Turing degree of a function which parametrizes the collection of all functions whose degree is in the given class. I prove that if a is a uniform upper bound on an ideal of degrees then a is the jump of a degree c with this additional property: there is a uniform bound b<a so that b V c < a.
    Remove from this list |
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  13. Véronique Izard, Pierre Pica, Elizabeth S. Spelke & Stanislas Dehaene (2008). Exact Equality and Successor Function: Two Key Concepts on the Path Towards Understanding Exact Numbers. Philosophical Psychology 21 (4):491 – 505.
    Humans possess two nonverbal systems capable of representing numbers, both limited in their representational power: the first one represents numbers in an approximate fashion, and the second one conveys information about small numbers only. Conception of exact large numbers has therefore been thought to arise from the manipulation of exact numerical symbols. Here, we focus on two fundamental properties of the exact numbers as prerequisites to the concept of EXACT NUMBERS : the fact that all numbers can be generated by (...)
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  14. Catherine Rowett (2013). Philosophy's Numerical Turn: Why the Pythagoreans' Interest in Numbers is Truly Awesome. In Dirk Obbink & David Sider (eds.), Doctrine and Doxography: Studies on Heraclitus and Pythagoras. De Gruyter. 3-32.
    Philosophers are generally somewhat wary of the hints of number mysticism in the reports about the beliefs and doctrines of the so-called Pythagoreans. It's not clear how much Pythagoras himself (as opposed to his later followers) indulged in speculation about numbers, or in more serious mathematics. But the Pythagoreans whom Aristotle discusses in the Metaphysics had some elaborate stories to tell about how the universe could be explained in terms of numbers—not just its physics but perhaps morality too. Was this (...)
    Remove from this list | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  15. Mark Sharlow, Generalizing the Algebra of Physical Quantities.
    In this paper, I define and study an abstract algebraic structure, the dimensive algebra, which embodies the most general features of the algebra of dimensional physical quantities. I prove some elementary results about dimensive algebras and suggest some directions for future work.
    Remove from this list | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  16. Richard Zach (2007). First-Order Gödel Logics. Annals of Pure and Applied Logic 147 (1):23-47.
    First-order Gödel logics are a family of finite- or infinite-valued logics where the sets of truth values V are closed subsets of [0,1] containing both 0 and 1. Different such sets V in general determine different Gödel logics GV (sets of those formulas which evaluate to 1 in every interpretation into V). It is shown that GV is axiomatizable iff V is finite, V is uncountable with 0 isolated in V, or every neighborhood of 0 in V is uncountable. Complete (...)
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation