In Axiomatic Theory of Formulas: Algebraic Theory of Formulas (Mathematics), author Victor Lvovich Porton introduces the axiomatic theory of formulas, a novel approach to understanding and describing mathematical objects. This framework encompasses formulas from various mathematical disciplines, with a specific focus on propositional formulas in mathematical logic.

The core concept of the Formula Operator Theory is presented, offering the potential to streamline proofs of mathematical theorems. This theory positions Formula Theory as a foundational paradigm for mathematics, laying the groundwork for future mathematical endeavors.

Formulated within this framework, objects are defined as formulas with distinct components, allowing for complex structures without violating the principle of non-self-reference (i.e., loops and other infinite structures are permitted).

Author Victor Porton uses concise and effective language, expressing complex mathematical concepts through a limited set of definitions and theorems. He aims to foster a deeper understanding of the relationship between mathematical notation and the underlying ideas.

While acknowledging the potential for exploration and inquiry, the book emphasizes the importance of maintaining a rigorous and grounded approach in mathematical exploration.

Axiomatic Theory of Formulas: Algebraic Theory of Formulas (Mathematics) aimed at presenting uncompromisingly rigorous and accurate facts, demonstrating that formalism and inductive explanations operate within distinct yet complementary domains.