Kurt Gdel was a _(person), mathematician, who worked on many foundational issues in formal logic. Some of his most interesting results are:
<ul>
<li>Gdelization, as a procedure to _(bootstrap) a representation of a formal system inside the formal system itself.</li>
<li>The completeness theorem of the predicate calculus, which proves that the theorems of the predicate calculus are all and only the logically valid formulas.</li>
<li>The incompleteness theorem for first order theories sufficiently powerful to express arithmetics, which states that if a theory of this kind is consistent it is also incomplete, i.e. there are statements which cannot be neither proved nor disproved in it.</li>
<li>The proof that, given a formal theory that can express arithmetics, if we bootstrap in it a proposition expressing the consistency of the theory itself, this proposition cannot be proved in the theory, unless we adopt a definition of "proposition expressing the consistency of the theory itself" based on stronger hypotheses than those on which the formal theory is based upon.
</ul>
Note that the above descriptions are by no way rigorous. The interested reader should refer to a good textbook on formal logic.
