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The Elements of Mathematical Logic Paperback – October 12, 2005


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Product Details

  • Paperback: 224 pages
  • Publisher: Dover Publications (October 12, 2005)
  • Language: English
  • ISBN-10: 0486446174
  • ISBN-13: 978-0486446172
  • Product Dimensions: 8.7 x 5.5 x 0.4 inches
  • Shipping Weight: 8 ounces (View shipping rates and policies)
  • Average Customer Review: 3.5 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #2,904,905 in Books (See Top 100 in Books)

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1 of 1 people found the following review helpful By Alan U. Kennington on November 17, 2013
Format: Paperback Verified Purchase
This 1950 book "The Elements of Mathematical Logic" by Paul Charles Rosenbloom is quite quirky in many ways, but it has many useful historical and philosophical insights. It is not suitable as a 21st century introduction to logic. It is mostly of value as historical and motivational background for concepts which have been learned in a more modern way, in a more modern notation. Of particular interest, in my opinion, is the intertwining of semantic and linguistic axioms in a way which is not often seen.

Rosenbloom claims in the preface to present the "most important approaches" to mathematical logic. This may have been true in 1950. There are indeed several different approaches in this book, but these don't seem to be a full survey of the subject. For example, the Gentzen natural deduction approach seems to be absent. The 1963 book "Foundations of Mathematical Logic" by Curry has a very credible claim to cover "the most important approaches", and Curry's book is much more substantial and more modern.

The content of this book by Rosenbloom includes the following.
* Page 1. A set of 20 axioms for propositional logic. Then many theorems from these.
* Page 9. A Boolean algebra of classes, emphasizing closure of both the space of propositions and the space of objects.
* Axiomatisation of Boolean algebra.
* Metatheorems about Boolean algebra.
* Page 21. Zorn's lemma is presented as an axiom!
* Pages 28-51. Propositional logic. Uses truth tables, then axioms and logical deduction.
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3 of 4 people found the following review helpful By Customer on October 23, 2010
Format: Paperback
I bought this because it has brief treatments of combinatory logic and the lambda calculus. I was dissapointed, however, because of the rather idiosyncratic notation; I had to go back and start nearly from the beginning to see how he was developing his formal systems. I've had logic, so I felt that it was inconvenient to have to read chapters just to get a handle on his notation and outlook. When I did finally arive at the sections on combinators and lambda, the treatment was too superficial to be a benefit. Should've just bought Hindley.

The problems stated, I found the author's discussion of early research informative and interesting. This book was written before an interpretation was formally defined in Tarski (1956), so the different research directions to escape this problem I thought were neat. There is much discussion about purely syntactical systems vs. systems where semantics are defined.
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