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Explicit mathematics: power types and overloading

Thomas Studer
2005 Annals of Pure and Applied Logic  
Thus establishing the concistency our system of explicit mathematics.  ...  This is a very general form of type dependent computation which occurs in the study of object-oriented programming languages. We also present a set-theoretic interpretation for monotone power types.  ...  We would like to thank Gerhard Jäger and Thomas Strahm for many helpful comments on an earlier version of this paper.  ... 
doi:10.1016/j.apal.2004.12.002 fatcat:4owxbrh5sval7py3evkbctwbuy

Page 2749 of Mathematical Reviews Vol. , Issue 98E [page]

1998 Mathematical Reviews  
proof-theoretic strength of monotone induction in explicit mathematics.  ...  Inductive definitions form a powerful but constructively acceptable principle, and so the reason for the interest in understanding this principle over explicit mathematics is obvious.  ... 

Page 1697 of Mathematical Reviews Vol. , Issue 2004c [page]

2004 Mathematical Reviews  
theory with only one universal set).  ...  Although the paper under review is related to Feferman’s program of “explicit mathematics”, the results it contains can be understood without much prior knowledge of explicit mathematics.  ... 

Polynomials Defined by Generating Relations

R. P. Boas, R. C. Buck
1956 The American mathematical monthly  
A Note on Grandsire Triples, London, 1886. (This is reprinted in Grand- sire, J. W. Snowden, London, 1905.) 4. Hamilton, W. R. Quarterly Journal of Mathematics, London, 1862, vol.  ...  Let A(w), y(t), g(w) be the formal power series (2) are Pr ages * This investigation was supported in part by the Office of Ordnance Research. t Sheffer [5], [6] calls them sets of type zero; Steffensen  ... 
doi:10.2307/2310587 fatcat:6q7nvdmfvzfvph6amdwhdc2tby

Page 626 of The American Mathematical Monthly Vol. 63, Issue 9 [page]

1956 The American Mathematical Monthly  
A Note on Grandsire Triples, London, 1886. (This is reprinted in Grand- sire, J. W. Snowden, London, 1905.) 4. Hamilton, W. R. Quarterly Journal of Mathematics, London, 1862, vol.  ...  Let A(w), y(t), g(w) be the formal power series (2) are Pr ages * This investigation was supported in part by the Office of Ordnance Research. t Sheffer [5], [6] calls them sets of type zero; Steffensen  ... 

Page 8788 of Mathematical Reviews Vol. , Issue 2002M [page]

2002 Mathematical Reviews  
Explicit mathematics was introduced by S. Feferman in the mid- 1970s as a framework for constructive mathematics.  ...  Here the author presents a new interpretation R, for realization, of second- order arithmetic in explicit mathematics.  ... 

A comparison of variant theories of intact biochemical systems. II. flux-oriented and metabolic control theories

Albert Sorribas, Michael A. Savageau
1989 Mathematical Biosciences  
In the past two decades, several theories, all ultimately based upon the same power-law formalism, have been proposed to relate the behavior of intact biochemical systems to the properties of their underlying  ...  The results allow one to make clear distinctions among the variant theories.  ...  The general set of constraint relationships that are valid in the power-law formalism already are implicit in the steady-state solution [33, 371.  ... 
doi:10.1016/0025-5564(89)90065-5 pmid:2520169 fatcat:7ejvioawe5fehmimhhsgslpvnq

Page 164 of Journal of the Association for Computing Machinery Vol. 6, Issue 2 [page]

1959 Journal of the Association for Computing Machinery  
The mathematical equivalent of the problem is to determine whether the matrix of the set of relations is nilpotent (converges to zero in its powers).  ...  The method hitherto used consists of making explicit all the implications of the set of relations (raising the matrix to higher powers until some power van- ishes) and verifying that no implication asserts  ... 

Page 4452 of Mathematical Reviews Vol. , Issue 99g [page]

1999 Mathematical Reviews  
Summary: “We show that in explicit mathematics the strong power type axiom is inconsistent with (uniform) elementary comprehen- sion and discuss some general aspects of power types in explicit mathematics  ...  in explicit mathematics?  ... 

Page 595 of American Society of Civil Engineers. Collected Journals Vol. 113, Issue 4 [page]

1987 American Society of Civil Engineers. Collected Journals  
Following the pattern of these previous developments, this paper presents sets of one-dimensional explicit upward water infiltration equa- tions in power-law form, expressing the one-dimensional upward  ...  Asstract: Equations expressed in explicit power algebraic forms for one-dimensional upward water movement, cumulative infiltration, and infiltration rate have been derived.  ... 

EXPLICIT MATHEMATICS AND OPERATIONAL SET THEORY: SOME ONTOLOGICAL COMPARISONS

GERHARD JÄGER, RICO ZUMBRUNNEN
2014 Bulletin of Symbolic Logic  
We discuss several ontological properties of explicit mathematics and operational set theory: global choice, decidable classes, totality and extensionality of operations, function spaces, class and set  ...  Also, the weak power type axiom is not really in the spirit of explicit mathematics since the selection of the names of the subtypes that go into the power type is not made explicit.  ...  Although OST itself does not include an axiom for power sets, operational set theory -in contrast to explicit mathematics -provides an ideal framework for introducing them.  ... 
doi:10.1017/bsl.2014.21 fatcat:bd2wiphc2jchlm7x7tiuxy7o6y

Page 2754 of Mathematical Reviews Vol. , Issue 97E [page]

1997 Mathematical Reviews  
97e:03075 Feferman’s explicit mathematics”. The paper thus gives the answer to Feferman’s conjecture. In one word, the power set axiom does not strengthen the systems.  ...  One can then obtain results (Section 8) such as EMo | +(Pow) =p: EMo |. At the end, the author asks a question concerning the strong power set axiom.  ... 

Page 2890 of Mathematical Reviews Vol. , Issue 2001E [page]

2001 Mathematical Reviews  
In this clearly and carefully written paper the authors study ver- sions of the power set axiom in the context of explicit mathematics, the family of axiomatic theories developed by Feferman and others  ...  The authors take up the further ques- tion of what exactly one needs for the refutation of the strong power set axiom and consider some theories even weaker than BAT.  ... 

Using FluidMath to Explore Recursive and Explicit Functions

Maria L. Hernandez, Nils Ahbel
2013 Mathematics Teacher  
Her focus is on using realworld applications and various technologies to help students see the power of mathematics.  ...  The next step in considering this set of recursive equations might be to write a closed-form, or explicit, function representing the problem.  ... 
doi:10.5951/mathteacher.106.6.0468 fatcat:ybgmkitpp5e3rm5jz3umuaztq4

Explicit construction of exponential sized families of k-independent sets

N Alon
1986 Discrete Mathematics  
= k, there are elements in all the members of A and not in the members of B.  ...  Error correcting codes are used to describe explicit collections Fk of subsets of {1, 2,... n}, with IFkl > 2 ckn (ck > 0), such that for any selections A, B of kl and k 2 of members of Fk with kl + k2  ...  Note added in proof Poljak, Pultr and R6dl [6, Theorem 3.7] gave explicit k-independent collections of almost exponential size.  ... 
doi:10.1016/0012-365x(86)90161-5 fatcat:erejdyro5bgzneac5hkf675gqi
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