scholarly journals Random reals, the rainbow Ramsey theorem, and arithmetic conservation

2013 ◽  
Vol 78 (1) ◽  
pp. 195-206 ◽  
Author(s):  
Chris J. Conidis ◽  
Theodore A. Slaman
Keyword(s):  
Ramsey Theorem ◽  
First Order ◽  
Base Theory ◽  
Random Reals

AbstractWe investigate the question “To what extent can random reals be used as a tool to establish number theoretic facts?” Let 2-RAN be the principle that for every real X there is a real R which is 2-random relative to X. In Section 2, we observe that the arguments of Csima and Mileti [3] can be implemented in the base theory RCA0 and so RCA0 + 2-RAN implies the Rainbow Ramsey Theorem. In Section 3, we show that the Rainbow Ramsey Theorem is not conservative over RCA0 for arithmetic sentences. Thus, from the Csima–Mileti fact that the existence of random reals has infinitary-combinatorial consequences we can conclude that 2-RAN has non-trivial arithmetic consequences. In Section 4, we show that 2-RAN is conservative over RCA0 + BΣ2 for -sentences. Thus, the set of first-order consequences of 2-RAN is strictly stronger than P− + IΣ1 and no stronger than P− + BΣ2.

Finite injury and Σ1-induction

1989 ◽  
Vol 54 (1) ◽  
pp. 38-49 ◽  
Author(s):  
Michael Mytilinaios
Keyword(s):  
First Order ◽  
Base Theory ◽  
Order Arithmetic

AbstractWorking in the language of first-order arithmetic we consider models of the base theory P−. Suppose M is a model of P− and let M satisfy induction for Σ1-formulas. First it is shown that the Friedberg-Muchnik finite injury argument can be performed inside M, and then, using a blocking method for the requirements, we prove that the Sacks splitting construction can be done in M. So, the “amount” of induction needed to perform the known finite injury priority arguments is Σ1-induction.

scholarly journals The modified Ramsey theorem is not a G_del sentence

2013 ◽  
Vol 19 ◽  
pp. 33-38
Author(s):  
Я.  Хинтикка
Keyword(s):  
Ramsey Theorem ◽  
First Order ◽  
If Logic

G_delian sentences are self-referential first-order sentences in the language of arithmetics. Perhaps the most celebrated one is the sentence which asserts its own unprovability. It is well known that this sentence is neither provable nor refutable in PA (Peano Arithmetics). Some logicians and philosophers have complained that such a sentence is difficult to grasp given its ‘meta-theoretical’ content and they started to look for undecidable arithmetical statements which have a combinatorial content. One such sentence is a variant of Ramsey’s sentence: the Paris-Harrington theorem asserts its undecidability. In the present paper I shall argue that such a sentence is not first-order expressible and thereby it does not provide the desired example of a combinatorial, undecidable arithmetical sentence. Instead I shall argue that it is expressible in Independence-friendly (IF) logic.

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

Stochasting modeling of planetary ring systems

1984 ◽  
Vol 75 ◽  
pp. 461-469 ◽  
Author(s):  
Robert W. Hart
Keyword(s):  
Maximum Entropy ◽  
Ring System ◽  
The Sun ◽  
Ultimate State ◽  
Interparticle Interactions ◽  
Ring Systems ◽  
First Order ◽  
Planetary Ring ◽  
Insight Into

ABSTRACTThis paper models maximum entropy configurations of idealized gravitational ring systems. Such configurations are of interest because systems generally evolve toward an ultimate state of maximum randomness. For simplicity, attention is confined to ultimate states for which interparticle interactions are no longer of first order importance. The planets, in their orbits about the sun, are one example of such a ring system. The extent to which the present approximation yields insight into ring systems such as Saturn's is explored briefly.

Morphological studies of linear (AB)n multiblock copolymers and their blends

1992 ◽  
Vol 50 (1) ◽  
pp. 384-385
Author(s):  
Richard J. Spontak ◽  
Steven D. Smith ◽  
Arman Ashraf
Keyword(s):  
Electron Microscopy ◽  
Microphase Separation ◽  
Multiblock Copolymers ◽  
First Order ◽  
Morphological Studies ◽  
Transmission Electron ◽  
First Order Phase Transition ◽  
Covalently Bonded ◽  
Total Molecular Weight ◽  
First Order Phase

Block copolymers are composed of sequences of dissimilar chemical moieties covalently bonded together. If the block lengths of each component are sufficiently long and the blocks are thermodynamically incompatible, these materials are capable of undergoing microphase separation, a weak first-order phase transition which results in the formation of an ordered microstructural network. Most efforts designed to elucidate the phase and configurational behavior in these copolymers have focused on the simple AB and ABA designs. Few studies have thus far targeted the perfectly-alternating multiblock (AB)n architecture. In this work, two series of neat (AB)n copolymers have been synthesized from styrene and isoprene monomers at a composition of 50 wt% polystyrene (PS). In Set I, the total molecular weight is held constant while the number of AB block pairs (n) is increased from one to four (which results in shorter blocks). Set II consists of materials in which the block lengths are held constant and n is varied again from one to four (which results in longer chains). Transmission electron microscopy (TEM) has been employed here to investigate the morphologies and phase behavior of these materials and their blends.

Exact First Order Finite Element Modeling for Eddy Current NDE

1991 ◽  
Vol 3 (1) ◽  
pp. 235-253 ◽  
Author(s):  
L. D. Philipp ◽  
Q. H. Nguyen ◽  
D. D. Derkacht ◽  
D. J. Lynch ◽  
A. Mahmood
Keyword(s):  
Finite Element ◽  
Finite Element Modeling ◽  
Eddy Current ◽  
Element Modeling ◽  
First Order ◽  
Eddy Current Nde

Challenging the Multidimensional Conception of Perceived Person-Environment Fit

2020 ◽  
pp. 1-9
Author(s):  
Julian M. Etzel ◽  
Gabriel Nagy
Keyword(s):  
Higher Education ◽  
University Students ◽  
Educational Outcomes ◽  
Factor Model ◽  
Higher Order ◽  
Substantial Proportion ◽  
Unique Variance ◽  
First Order ◽  
Person Environment Fit ◽  
Order Factor

Abstract. In the current study, we examined the viability of a multidimensional conception of perceived person-environment (P-E) fit in higher education. We introduce an optimized 12-item measure that distinguishes between four content dimensions of perceived P-E fit: interest-contents (I-C) fit, needs-supplies (N-S) fit, demands-abilities (D-A) fit, and values-culture (V-C) fit. The central aim of our study was to examine whether the relationships between different P-E fit dimensions and educational outcomes can be accounted for by a higher-order factor that captures the shared features of the four fit dimensions. Relying on a large sample of university students in Germany, we found that students distinguish between the proposed fit dimensions. The respective first-order factors shared a substantial proportion of variance and conformed to a higher-order factor model. Using a newly developed factor extension procedure, we found that the relationships between the first-order factors and most outcomes were not fully accounted for by the higher-order factor. Rather, with the exception of V-C fit, all specific P-E fit factors that represent the first-order factors’ unique variance showed reliable and theoretically plausible relationships with different outcomes. These findings support the viability of a multidimensional conceptualization of P-E fit and the validity of our adapted instrument.

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