{"product_id":"introduction-to-mathematical-logic-set-theory-computable-functions","title":"Introduction to Mathematical Logic: Set Theory Computable Functions","description":"\u003cp\u003eIn this review the reviewer assesses Introduction to Mathematical Logic as a deliberate, rigorous undergraduate to beginning graduate text that aims to guide readers through three core areas: \u003cstrong\u003eset theory\u003c\/strong\u003e, computable functions, and model theory. The bottom line is that this book is best for students who want a logically paced, mathematically precise introduction without heavy prerequisites; its biggest reason to buy is the way it builds each part slowly at first and then accelerates to cover substantive topics useful for further study.\u003c\/p\u003e\n\u003ch2\u003eKey Features\u003c\/h2\u003e\n\u003cul\u003e\n \u003cli\u003e\n\u003cstrong\u003eThree-part structure:\u003c\/strong\u003e The book divides material into set theory, computable function theory, and model theory so readers can focus on one logical area at a time.\u003c\/li\u003e\n \u003cli\u003e\n\u003cstrong\u003eAccessible prerequisites:\u003c\/strong\u003e Virtually no formal prerequisites are required, making it suitable for advanced undergraduates stepping into logic.\u003c\/li\u003e\n \u003cli\u003e\n\u003cstrong\u003eGradual progression:\u003c\/strong\u003e Each part starts slowly to establish notation and concepts, then increases in pace to introduce more complex ideas and connections.\u003c\/li\u003e\n \u003cli\u003e\n\u003cstrong\u003eMotivational algebraic context:\u003c\/strong\u003e Familiarity with basic abstract algebra concepts such as groups, rings, and fields is referenced to motivate topics in the later sections.\u003c\/li\u003e\n \u003cli\u003e\n\u003cstrong\u003eIntroductions to current topics:\u003c\/strong\u003e Each part concludes with brief introductions to selected topics of current interest, providing pathways for further reading.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eWho It's For\u003c\/h2\u003e\n\u003cp\u003eThis text is aimed at senior undergraduates and beginning graduate students in mathematics who want a single-volume introduction to logical foundations across \u003cstrong\u003eset theory\u003c\/strong\u003e, computability, and model theory. It works well for students who have seen basic abstract algebra and want a mathematically precise, theorem-driven presentation rather than a survey.\u003c\/p\u003e\n\u003cp\u003eReaders who need a gentle, non-technical primer or a classroom workbook with numerous exercises and solutions should look elsewhere; the book is oriented toward formal development and concise exposition rather than extensive hand-holding.\u003c\/p\u003e\n\u003ch2\u003ePros \u0026amp; Cons\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003ePros\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n \u003cli\u003eWell organized into three clear parts, which helps learners approach each topic in sequence.\u003c\/li\u003e\n \u003cli\u003eMinimal prerequisites make it accessible to motivated undergraduates transitioning into graduate-level logic.\u003c\/li\u003e\n \u003cli\u003eThe initial slow development of concepts eases readers into formal notation and arguments.\u003c\/li\u003e\n \u003cli\u003eEach part's brief introduction to current topics points readers toward modern directions in the field.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp\u003e\u003cstrong\u003eCons\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n \u003cli\u003eThe treatment accelerates in later sections and may assume comfort with abstract reasoning, which can challenge readers seeking a gentler pace.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eSpecifications\u003c\/h2\u003e\n\u003ctable\u003e\n \u003ctr\u003e\n\u003ctd\u003eTitle\u003c\/td\u003e\n\u003ctd\u003eIntroduction to Mathematical Logic: Set Theory Computable Functions Model Theory\u003c\/td\u003e\n\u003c\/tr\u003e\n \u003ctr\u003e\n\u003ctd\u003eAuthor\u003c\/td\u003e\n\u003ctd\u003eJerome Malitz\u003c\/td\u003e\n\u003c\/tr\u003e\n \u003ctr\u003e\n\u003ctd\u003eIntended level\u003c\/td\u003e\n\u003ctd\u003eUndergraduate senior or beginning graduate\u003c\/td\u003e\n\u003c\/tr\u003e\n \u003ctr\u003e\n\u003ctd\u003eParts covered\u003c\/td\u003e\n\u003ctd\u003eSet theory; computable function theory; model theory\u003c\/td\u003e\n\u003c\/tr\u003e\n \u003ctr\u003e\n\u003ctd\u003ePrerequisites\u003c\/td\u003e\n\u003ctd\u003eVirtually none; familiarity with basic abstract algebra helpful\u003c\/td\u003e\n\u003c\/tr\u003e\n \u003ctr\u003e\n\u003ctd\u003eApproach\u003c\/td\u003e\n\u003ctd\u003eSlow start per part with increasing pace and complexity\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\n\u003ch2\u003eOur Verdict\u003c\/h2\u003e\n\u003cp\u003eIntroduction to Mathematical Logic is a solid, value-minded text for students who want a rigorous, structured entry into logic across set theory, computability, and model theory. Its deliberate pacing at the start of each part and succinct introductions to contemporary topics make it a good next-step book for advanced undergraduates and beginning graduate students preparing for deeper study.\u003c\/p\u003e\n\u003ch2\u003eFrequently Asked Questions\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003eIs this book suitable for someone with only basic algebra?\u003c\/strong\u003e\u003cbr\u003eYes. The book requires virtually no formal prerequisites, though familiarity with groups, rings, and fields can help motivate some topics.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eDoes the text cover model theory in depth?\u003c\/strong\u003e\u003cbr\u003eIt covers model theory as one of three main parts and relies on concepts developed earlier, offering a concise but substantive introduction rather than an exhaustive treatment.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eWill this serve as a self-study resource?\u003c\/strong\u003e\u003cbr\u003eIt can be used for self-study by motivated readers, but those seeking many worked examples or a very gentle pace may prefer supplementary materials.\u003c\/p\u003e","brand":"Jerome Malitz","offers":[{"title":"Default Title","offer_id":48613439144155,"sku":"1461394430","price":54.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0724\/1043\/1707\/files\/61w4K9pSreL._SL1307.jpg?v=1778418799","url":"https:\/\/gearmusthave.com\/products\/introduction-to-mathematical-logic-set-theory-computable-functions","provider":"GearMustHave","version":"1.0","type":"link"}