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Description
Computability and UnsolvabilityIn this classic text, Dr. Davis provides a clear introduction to computability, at an advanced undergraduate level, that serves the needs of specialists and non specialists alike. In Part One (Chapters 1 5), Professor Davis outlines the general theory of computability, discussing such topics as computable functions, operations on computable functions, recursive functions, Turing machines, self applied, and unsolvable decision problems. The author has
In this classic text, Dr. Davis provides a clear introduction to computability, at an advanced undergraduate level, that serves the needs of specialists and non-specialists alike.In Part One (Chapters 1-5), Professor Davis outlines the general theory of computability, discussing such topics as computable functions, operations on computable functions, recursive functions, Turing machines, self-applied, and unsolvable decision problems. The author has been careful, especially in the first seven chapters, to assume no special mathematical training on the part of the reader.
Part Two (Chapters 6-8) comprises a concise treatment of applications of the general theory, incorporating material on combinatorial problems, Diophantine Equations (including Hilbert's Tenth Problem) and mathematical logic. The final three chapters (Part 3) present further development of the general theory, encompassing the Kleene hierarchy, computable functionals, and the classification of unsolvable decision problems.
When first published in 1958, this work introduced much terminology that has since become standard in theoretical computer science. Indeed, the stature of the book is such that many computer scientists regard it as their theoretical introduction to the topic. This new Dover edition makes this pioneering, widely admired text available in an inexpensive format.
For Dover's edition, Dr. Davis has provided a new Preface and an Appendix, "Hilbert's Tenth Problem Is Unsolvable," an important article he published in The American Mathematical Monthly in 1973, which was awarded prizes by the American Mathematical Society and the Mathematical Association of America. These additions further enhance the value and usefulness of an "unusually clear and stimulating exposition" (Centre National de la Recherche Scientifique, Paris) now available for the first time in paperback.
Binding Type: Paperback
Publisher: Dover Publications
Published: 12/01/1985
ISBN: 9780486614717
Pages: 288
Weight: 0.65lbs
Size: 8.46h x 5.44w x 0.57d
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★★★★★ 3
No information on active ingredients.
Size: 4 Ounce (Pack of 4), Set name: Adult Mint
Gave 3 starts as an act of goodwill . The toothpaste does not specify the type or percentage of active ingredients it contains. For a beneficial effect, the concentration of nano-hydroxyapatite should be 10% or higher. Based on indirect information, this product appears to contain only about 4.2%.
The manufacturer did not respond to inquiries regarding the active ingredient content, which is concerning.
Additionally, the toothpaste has an unusual taste that is definitely not mint.
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Reviewed in the United States on April 21, 2026
★★★★★ 5
Great for Sensitive Teeth & Leaves My Mouth Feeling Clean
Size: Pack of 1, 4 Ounce, Set name: B. Whitening
Really impressed with the Boka Fluoride Free Toothpaste.
It has a clean, refreshing mint flavor without being overpowering, and it feels much gentler on sensitive teeth than other toothpastes I’ve tried.
My teeth feel smooth and clean after using it, and I like that the ingredients are simple and fluoride free. Definitely something I’ll keep repurchasing.
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Reviewed in the United States on May 25, 2026
★★★★★ 5
Clean Ingredients & Leaves Teeth Feeling Smooth
Size: Pack of 1, 4 Ounce, Set name: B. Whitening
I’ve tried many natural toothpastes, and this one quickly became a favorite. The texture feels smooth, and my teeth feel really clean after brushing. I love that it contains nano hydroxyapatite and is fluoride-free, especially for sensitive teeth.
The flavor is fresh without being overpowering, and it doesn’t leave a weird aftertaste. It’s also gentle enough for everyday use and makes my teeth feel polished and healthy. Definitely worth trying if you want a cleaner alternative toothpaste.
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Reviewed in the United States on May 20, 2026
★★★★★ 5
Perfect Fluoride alternative
Size: Pack of 1, 4 Ounce, Set name: B. Whitening
I bought this because it's popular in other countries like Japan. America is so behind using fluoride, when it's been proven to cause pituitary gland problems. If you're looking for a fluoride-free toothpaste look no further.
It works well, you just unscrew and apply to your brush. Pro tip: use a sonic toothbrush and glide on your teeth at a 45° angle. Using this toothpaste for months, 2 minutes twice a day, has made my teeth visibly whiter.
The flavor is not super strong, so it's suitable for kids and really anyone. Super easy and simple to use, it works like regular toothpaste. Smells minty, it's fluoride-free, and medium sized. It'll last me about 2 months, which I find worth it.
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Reviewed in the United States on April 28, 2026
★★★★★ 4
Fluoride who?
Size: Pack of 3, 4 Ounce, Set name: B. Whitening
Great product definitely works better than your traditional fluoride or fluoride free toothpaste it actually combats plaque and strengthens the enamel of your teeth I have physically and visibly seen the difference not just in my teeth but gums. Tastes great cleans well clean ingredients the only downside is it's unfortunately very pricey and if you're buying for not just yourself but a family it can start to add up fast just something to consider before purchasing. I love the tube and cap design it's gentle on your gums and teeth and it has good ingredients making the minty flavor taste more natural rather than a synthetic mint flavor and this product actually whitens your teeth. keep in mind that this isn't a replacement for teeth whitening treatments and it's also not a replacement for good dental hygiene like flossing/brushing multiple times a day. If your suffering from serious Dental issues this will not cure it but it is an excellent alternative to fluoride toothpaste that provide little to no benefit for your actual oral and overall dental health. The reason for four not five stars is because of the price I think if they could continue making the same product got the same level of quality for a little less money it would be a five-star item
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Reviewed in the United States on March 8, 2026