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- Richard Sommer
- Ann. Pure Appl. Logic
- 1995

The relative strengths of first-order theories axiomatized by transfinite induction, for ordinals less-than ~0, and formulas restricted in quantifier complexity, is determined. This is done, in part, by describing the provably recursive functions of such theories. Upper bounds for the provably recursive functions are obtained using model-theoretic… (More)

- FRANK W. PUTNAM, ARTHUR M. SQUIRES, +9 authors MARGARET STERLING
- 2005

Science serves its readers as a forum for the presentation and discussion of important issues related to the advance-The de ment of science, including the presentation of minority or ly condu conflicting points of view, rather than by publishing only .i. material on which a consensus has been reached. Accord-OlflOfl ingly, all articles published in… (More)

- FRANK W. PUYNANI, H. S. GUTOWSKY, ARTHUR D. HASLER, RUDOLF KOMPFNER, RICHARD SOMMER
- 2005

Science serves its readers as a forum for the pi-esentation and discussion of important issues related to the advancement of science, including the presentation of minority or conflicting points of view, rather than by publishing only material on which a consensus has been reached. Accordingly , all articles published in Science-including editorials, news… (More)

- David McMath, Marianna Rozenfeld, Richard Sommer
- LPAR
- 2001

The EPGY Theorem-Proving Environment is designed to help students write ordinary mathematical proofs. The system, used in a selection of computer-based proof-intensive mathematics courses, allows students to easily input mathematical expressions, apply proof strategies , verify logical inference, and apply mathematical rules. Each course has its own… (More)

- Jeremy Avigad, Richard Sommer
- Bulletin of Symbolic Logic
- 1997

We describe a model-theoretic approach to ordinal analysis via the finite com-binatorial notion of an α-large set of natural numbers. In contrast to syntactic approaches that use cut elimination, this approach involves constructing finite sets of numbers with com-binatorial properties that, in nonstandard instances, give rise to models of the theory being… (More)

- Richard Sommer, Gregory Nuckols
- J. Autom. Reasoning
- 2004

- Richard Sommer
- 1996

This paper provides a new proof of the consistency of a formal system similar to the one presented by Chuaqui and Suppes in 2, 9]. First, a simpler, yet in some respects stronger, system, called Elementary Re-cursive Nonstandard Analysis (ERNA) will be provided. Indeed, it will be shown that ERNA proves the main axioms of the Chuaqui and Sup-pes system.… (More)

- Jeremy Avigad, Richard Sommer
- J. Symb. Log.
- 1999

We use model-theoretic methods described in [3] to obtain ordinal analyses of a number of theories of first-and second-order arithmetic, whose proof-theoretic ordinals are less than or equal to Γ 0 .

- Andrew D Rosenberg, Jovan Popovic, +4 authors Germaine Cuff
- Regional anesthesia and pain medicine
- 2012

Simulation-based training is becoming an accepted tool for educating physicians before direct patient care. As ultrasound-guided regional anesthesia (UGRA) becomes a popular method for performing regional blocks, there is a need for learning the technical skills associated with the technique. Although simulator models do exist for learning UGRA, they either… (More)